This is a little outside my specialty area (modern cross-strait relations), but I think I can largely answer this question.
Perhaps the most important factor in understanding how the life of the average Taiwanese person changed with the KMT retreat is to remember that it had only been 4 years since the end of Japanese occupation. The Japanese had occupied Taiwan from 1895 to 1945, and had spent those 50 years improving Taiwan's infrastructure and enforcing Japanese language and cultural norms in the education system. A middle-aged farmer in 1949 would have grown up under Japanese rule, and been used to power structures and official political and social structures based on Japanese colonial systems. While Taiwan itself was not a battleground during WW2, both ethnically Chinese and aboriginal Taiwanese people were largely supportive of Japan during the war and military units were created from volunteers drawn from both groups. This attitude is especially significant given how negatively Japanese occupation has been viewed in other former colonies. I don't want to claim the Japanese occupation was purely benevolent, as it was still a colonial occupation, but suffice it to say that in 1945 (and even today) the view of the average Taiwanese person on Japan is decidedly more positive than the average mainland-Chinese resident. that
This is very important in understanding how massive a shift the arrival of approximately 2 million mainland-Chinese people would be for the existing Taiwanese population. While the KMT retreat was the result of the Chinese Civil War, the wounds of well over a decade of brutal warfare with Japan were still fresh in their minds. The KMT brought their bitter hatred of the Japanese with them to Taiwan, and institutionalized it almost immediately. Under KMT rule schools would immediately begin teaching that the Japanese were evil, and any positive references to Japanese occupation would be expunged. Political structures and the military and police leadership would suddenly be occupied by people who had spent most of their recent lives fighting the people who had previously occupied those positions. For the average Taiwanese person, regardless of their personal feelings about the Japanese, the cultural whiplash would be obvious.
Language on the island would also see a shift during this time. Until 1945 Japanese had been the only official language of Taiwan, with most non-Japanese also speaking Taiwanese Hokkien (a dialect originating in Fujian province), Hakka, or one of the Formosan Languages (aboriginal languages considered the precursors of most Polynesian languages). In 1945, Mandarin became the official language on the island, and was made compulsory in schools as well. Taiwanese Hokkien and aboriginal languages would continue to be tolerated in non-official contexts, but a clear class divide would appear between those who spoke Mandarin fluently (a mark of KMT association) and those who did not.
To compound all of these issues, life in Taiwan had already undergone additional massive upheaval in the years between 1945 and 1949, particularly in 1947 with the February 28 incident, sometimes referred to as 228. Under the Japanese there had been a flourishing of Taiwanese intellectual life, with an educated Taiwanese elite emerging as a force for a unique Taiwanese identity and calling for some element of self-rule long before the end of WWII. These groups had begun advocating for Taiwanese independence from the Republic of China shorty after the war ended, and were viewed as dissident and possibly revolutionary elements by the occupying KMT authorities. Given that they were already massively struggling to contain revolutionary elements on the mainland, the reaction to these groups was severe. Additionally, the occupying KMT authorities were perceived (accurately in most cases) as corrupt by most Taiwanese people due to imposed monopolies, takeovers of businesses that had been Taiwanese-operated before the war, and economic mismanagement that led to massive inflation.
The economic issues and growing independence movement created a powder keg environment that erupted on February 28, 1947 when a KMT Tobacco Monopoly agent struck a Taiwanese widow illegally hawking cigarettes on the street in Taipei. A confrontation between the agents and an angry crowd that witnessed the events spiraled into an island-wide uprising that, while violent at times, led to the establishment of Taiwanese-organized groups controlling much of the islands institutions and infrastructure. They submitted a list of demands to the occupying government including 32 reforms that would require more representation in the provincial administration from the 'native' Taiwanese population. The KMT authorities stalled for time until March 7, when ROC troops arrived from Fujian and began a bloody suppression of the uprising. By the end of March thousands of Taiwanese people had been killed, many more imprisoned without trial, and the KMT firmly in control once again. Most independence groups were declared illegal, often falsely labeled as sympathetic to the CCP, and their members were either executed, imprisoned, or fled to Hong Kong or to North America.
Martial law as declared during the February 28 incident, but was lifted by the end of March 1947. With the Retreat in 1949, however, Taiwan was officially labeled as part of the Civil War warzone by the KMT government, and martial law was reintroduced. It would persist until 1987, a period which would come to be called the "White Terror", during which groups that sought Taiwanese independence or the establishment of a Taiwanese identity separate from the KMT and mainland China would continue to be illegal and their members would often find themselves imprisoned in secret state political prisons. Refugees from the mainland would often be targeted as well, especially those without direct KMT ties. Any sign of dissent or calls for more democratic government could be taken as a threat to the KMT, and result in imprisonment or "disappearance." Several people who were imprisoned during this period would go on to become major political leaders during the post-White Terror reform period that saw Taiwan transition to democracy in 1987, including President Lee Teng-hui.
This is a great answer. I learned so much about Taiwan!