Qing Taiwan is occasionally thought of as a colonial space in academic literature (I'll get to that later). But this hasn't really established itself in the popular consciousness, and the issue is primarily historiographical.

In both the PRC and Taiwan, there is a very clear reluctance to display either China as a colonial power or the Han Chinese -- who, after all, make up almost 98% of the island's population -- as colonizers.

There are two main paradigms about Taiwan's conquest in the popular consciousness of China and Taiwan. The first paradigm is that China's civilizing influence attracted peripheral peoples and assimilated them into Han Chinese culture in what was essentially a peaceful and harmonious process. Or to quote one Chinese historian directly:

As an agrarian nation, China was essentially constructed not on the basis of military force or conquest; rather, [the Chinese state was founded] through trade based on the tribute system [and the spread of] rites and cultural enlightenment... and this system was established and sustained through several thousand years prior to the invasion of China by Western capitalists in the nineteenth century.

This is how both the Chinese Communist Party and the former military dictatorship of Taiwan saw the growth of Chinese territory. The assimilation of Taiwanese aborigines was considered part of the same pacifist process.

Furthermore, the island itself -- as indeed, most or all of what is now the PRC's territory -- was (at least implicitly) considered immemorially "Chinese" in some way. The victory of Koxinga over the Dutch was considered a triumphant expulsion of Western imperialists (never mind that the Chinese government had explicitly told the Dutch to go to Taiwan since it wasn't Chinese territory!) and the Japanese conquest in 1895 was seen as a tragedy.

Considering Taiwan as a colonial space simply does not jibe with this view of history. China was a victim of Western and Japanese imperialism; its expansion was ultimately a peaceful one; Taiwan was always Chinese in some sense. How, then, could China, a non-Western and generally peaceful nation, ever have colonized its own rightful territory?

With the democratization of Taiwan and the rise of its independence movement, new perspectives focus on the multicultural history of the island and the many ways in which it is not Chinese. This view of history would have a "Taiwanese" identity emerge under the Qing with the Han Chinese settlers of the island who eked out a living for themselves under the neglect or hostility of Beijing. But this perspective and its political implications would also be threatened by the notion that the Taiwanese -- by which the Hakka and Min Chinese, who make up 84% of the population, are generally meant -- were in fact colonists who essentially destroyed the indigenous cultures of lowland Taiwan. The Taiwanese aborigines are emphasized as yet another way in which Taiwan differs from China, but how the aborigines mixed with the Chinese settlers is emphasized over the bloody conflicts.

Hence Taiwan could not have been colonized.^1

In Western historiography, things are a little different. Early Western studies of the Qing centered on how and why they supposedly "failed" to adapt to the European intrusion. A typical work from this era is the 1958 work Confucian China and its Modern Fate, which claims to "focus on the Confucian intellectuals who were, by training and temperament, completely unable to confront the threat posed by the West." Qing history in general was not seen for its own merits, but for its supposed failures in the 19th century. Clearly, the Qing -- a failure of a dynasty -- could not then have been a colonial state. Colonialism was something Europeans (and the Japanese, who "succeeded") did.

This changed radically as the 20th century passed. Beginning in the 1980s, there was a huge change in how Western scholarship saw the Qing in general. The Qing were no longer seen as simply assimilated into Chinese culture; the Manchu character of the empire was paramount to its functioning. The Qing were no longer the complacent empire that the West had thought it to be; it was an aggressively expanding state that competed and gathered information on a continental scale. The Qing were no longer the "last Chinese dynasty," but "the most successful of all Early Modern dynasties." Productive comparisons were drawn to other Early Modern multicultural states, like Russia and the Ottomans.

And, yes, the Qing began to be studied as colonizers. This really began in 1998 when the acclaimed historian Peter Perdue declared in The International History Review that "the Qing empire in China was a colonial empire that ruled over a diverse collection of peoples with separate identities and deserves comparison with other [colonial] empires." This helped further a conceptual change of sorts. A selection of some of the better histories that exemplify this trend:

• Peter C. Perdue, China Marches West: The Qing Conquest of Central Eurasia (Harvard University Press, 2009): "Siberia offers many points of comparison with China's colonial domains in Central Asia, particularly Mongolia and Xinjiang... [S]everal scholars have examined the special characteristics of Qing rule in Mongolia, Xinjiang, and Tibet. They suggest grounds for comparison of the Qing state to other colonial empires."
• Nicola di Cosimo, "Qing Colonial Administration in Inner Asia" (published in 1998 in The International History Review, 20:2): "It may be possible to treat the Qing empire, and especially the history of its imperial expansion in Inner Asia, as an example of colonial rule... [Various features of the Qing administration of Mongolia, Tibet, and the Tarim Basin] bring it closer to its European counterparts and separate it from anything else in Chinese history."
• Laura Hostetler, Qing Colonial Enterprise: Ethnography and Cartography in Early Modern China (University of Chicago Press, 2005): "During the course of the seventeenth and eighteenth centuries, Guizhou province and other parts of the Qing empire were colonized by settlers who moved in to displace indigenous populations... [T]he administrative governance of the southwest in particular was changed in order to bring the area under direct control of the central government for the first time. As territory was being colonized, 'colonial' seems a reasonable adjective to use to describe the Qing. But even more, I choose to use the term to highlight the methods, technologies, and ideologies that the Qing employed in extending its geographical reach, and those used by European colonial powers during the same period."
• Donald S. Sutton, "Violence and Ethnicity on a Qing Colonial Frontier: Customary and Statutory Law in the Eighteenth-Century Miao Pale" (published in 2003 in Modern Asian Studies, 37:1): "The new [Qing administrative] system [in the southwest] produced a form of colonial relationship and in some respects Qing law resembled Western colonial forms... The effort to use indigenous law is one of the closest parallels with colonial systems, with their unequal coexisting legal systems. As recent scholars of such systems have noticed, one legal order is not simply imposed on the other, but both receive mutual influences and each produces codes or 'discourses' that can be turned to the varying purposes of colonizers, indigenes and settlers. These are the processes to be examined below in the Hunan/Guizhou border."

The same ideas are applied to Taiwan, although so far, Western scholarship on Qing colonialism has tended to focus on either Inner Asia or the southwestern mountains. Emma Teng's Taiwan's Imagined Geography: Chinese Colonial Travel Writing and Pictures, 1683-1895 is one of the few that focus on Qing "colonial discourse" (the eroticization of native women and the implicit portrayal of the settlement of Taiwan as a type of sexual domination over the feminine and emasculated natives, for example, which is also something Edward Said talked about in Orientalism) surrounding Taiwan specifically.

But in Western consciousness, the Qing (if they're even known) are still known largely as the failed dynasty they were made up to be a few decades ago, and colonialism is something only the West and Japan could do, for good or for bad (see /u/raggidimin's post where colonialism in Taiwan is immediately equated with the VOC and Japanese presence, for an illustration of this in this very thread). Hence the lack of knowledge about their colonization or at least colonial-ish practices.

^1 More on this, see Edward Vicker's article "Original Sin on the Island Paradise? Qing Taiwan's colonial history in comparative perspective" and "On the Impossibility of a Postcolonial Theory of Taiwan," Emma Teng's epilogue to Taiwan's Imagined Geography.

EDIT: /u/PangeranDipanagara has a far superior response further down in this thread. I suggest you read that response first.

Though it doesn't quite address the question you have in mind, I'd reject the notion that Taiwan isn't usually thought of as a product of colonization. Taiwanese nowadays (Han or not) certainly are aware of the island's colonial past. Fort Zeelandia, now known as Anping Fort, where Koxinga defeated the Dutch, who had settled Taiwan to trade in the region, is still preserved as a museum. The influence of Japanese rule after the Treaty of Shimonoseki is even more prominent; for example, the current Presidential Office Building originated as the residence built by the Japanese for the Governor-General of Taiwan.

The question you're asking is less historical per se than, loosely speaking, historiographic, in the sense that it's about how we write, talk or think about certain histories. It's also interdisciplinary because it concerns anthropology and/or sociology.

The relevant meta here is that we most readily imagine colonialism in terms of 1) European colonialism in the early modern period, and to a lesser extent, 2) the imperialism of the 19th- and early 20th centuries. As you and raggidimin noted already, Taiwan had its part in both of those two eras, with Dutch, Spanish and Japanese involvement.

Scholars do talk about different types of colonialism. The Han Chinese migration you're thinking of could be described as settler colonialism, in which populations move from the metropole to the colony in large numbers and permanently settle, eventually outnumbering the indigenous in some cases.

Keep in mind though, settler colonialism is perhaps not best understood as just a subtype of "classical" colonialism. In some ways, it is antithetical to the traditional framework of colonialism. There is a less dichotomous relationship between colony and metropole, for instance, and in the case of Taiwan, it was a prefecture and later a province under the Qing. There are also theoretical issues of how to parse the "native-settler" dichotomy, e.g., how long do a people have to settle somewhere -- and in what manner -- before they can be considered native? How do those people identify themselves?

If you're interested in settler colonialism, this provides a very brief intro and bibliography. And this from the AHA gives brief definitions of different kinds of colonialism. That list shouldn't be thought of as exhaustive or definitive, but it illustrates the kind of thinking scholars do in describing particular colonial situations.