I remember reading something about the spanish and their conversion efforts but weren't other countries in Asia Colonized by European Powers as well? Most seemed to have ended up with some form of either Islam, Buddhism or Hinduism why the Philippines holds a Strong Catholic Majority.
Still a valid question, but I just want to point out that the largest religion in South Korea is also Christianity (not nearly as strongly as in the Philippines, but still).
Others will give a better, more detailed answer, but it is for the same reason Latin America is predominantly Catholic, it was, for a long time, from 1521 till 1898, a Spanish colony.