Quite simply, the Philippine population was not immunologically naive to the diseases that Spanish visitors brought during conquest, which is a very different situation to that of the Americas.

Disease transmission is at its most basic a geometric progression problem. Due to various characteristics of population dynamics, the environment, the disease itself, and so on you end up with an overall average of the number of new infections caused by an individual who has become infectious. When that number is high the number of people infected grows rapidly in an "outbreak" scenario. When that number is below 1 consistently for an extended period the disease will eventually die out. When it's right around 1 it will stick around as an endemic disease.

When a disease is circulating in a given population the result is that some subset of that population will previously have been exposed to it and may have some degree of immunity to it. This not only lowers the basic reproduction number and slows the spread of the disease through the population, it also reduces the likelihood of the most severe symptoms (including death) among people who nevertheless become infected.

Anyway. Since the Philippines were plugged into the "global economy" prior to Spanish conquest they had already been exposed to all of the diseases the Spanish brought with them. Even if outbreaks did happen, they would have been less severe and had a diminished impact compared to if the island had been completely isolated. The Philippines had been part of many various sultanates and empires prior to Spanish conquest, and were fully integrated into the trade system of East and South East Asia (which was itself connected to South Asia and East Africa through Indian Ocean trade).

In contrast to the other two answers, replies to this old question imply that there were epidemics due to Spanish and that they were quite devastating. Notably there was this answer by u/boyohboyoboy

From the circumstantial evidence taking these into account, and Spanish records of smallpox and measles ravaging subject Filipino communities during the early colonial period, Newson concludes that while acute infections may indeed have been introduced from China (as from the other trade contacts of the archipelago), the low population densities in the Philippines did not enable these diseases to become endemic. And the tremendous suffering from these diseases experienced upon the advent of the Spaniards - who tended to require the Filipinos to live in concentrated population centers - indicates that the diseases' introduction in such circumstances was not something with a precedent in this scale before the colonial period.