The answer to this question is a lot more simple than you may realize. In the European colonies in Asia, "Indochina," Indonesia, India, the Philippines, Burma, and to a lesser extent Taiwan, colonialism took a very different turn than in the New World.

Colonialism in the new world was much more oriented towards settler colonialism. This was in part because settlers in the New World often pushed Native Americans off their land and further inland.

In the case of the Spanish, they did attempt to integrate natives into their colonies, primarily for labor with the econmienda system. However, many of the Native Americans died to various Old World diseases. It's unknown how many people died but it's estimated to be over 90 percent of the population or maybe 20 million people. I'm a bit fuzzy about these figures because I am an Asia expert and not a specialist in Latin American history.

So what about Asia or the Philippines? Well quite simply not enough people died of foreign diseases. Local languages remained dominate, at least in ordinary life. French, English, and Spanish became the administrative languages of course.

That's not to say that the Spanish did not bring settlers. 1200 Spanish families did settle around Manila in the 16th century for example. However, because there was no die off of native populations, there was little need to bring in settler populations. The exceptions to this maybe Burma or Taiwan.

There's an interesting discussion here about how local populations are integrated into colonial systems for labor. In Taiwan, it was very hard to integrate aboriginal people's into the colonial labor force. As such, the Dutch brought in Chinese immigrants from Fujian. This was also necessary in the New World for different reasons. African slaves and European homesteaders were brought in most of Latin America. This was not as necessary in Asian colonies like Vietnam or the Philippines.

One important thing to keep in mind, although today the Philippines has one major language, tagalog, this was not the case until relatively recently. The development of a national consciousness was an important factor in propagating the idea of a single national language. There are still a myriad of local languages and dialects in the Philippines. To study this I highly recommend Benedict Anderson's Imagined Communities.

I wish I could provide a better answer but I'm actually at an airport in Hanoi on spotty internet. I hope this helps.

Here is an old thread with a similar question