The answer is pretty straightforward: the Philippines were never isolated from the landmass of continental Asia, unlike the Americas. Therefore, diseases could spread from Asia to the Philippines with relative ease, from contacts with China, India and the Islamic World (as both Chinese and Islamic traders had established regular contacts with the Philippines well before Magellan set foot there).
For this reason, the advent of the Spanish did not have the devastating impact that they had in the New World, which had been isolated for much longer.
For pre-Spanish contacts, I would recommend Patanne, The Philippines in the Sixth to Sixteenth Centuries.
Interestingly, the earliest known document discovered in the Philippines - the Laguna Copperplate Inscription of around 900 ad - apparently refers to trading relationships with Sumatra. The interconnection of the Philippines and the rest of the world is very ancient.
To get the sorts of deadly "plagues" that we see in the Black Death or in the devastation of North American indigenous populations, pathology indicates you need two things. One, you need a source for these pathogens to come from, and two, you need a population large enough to foster these deadly diseases in. While North America indeed had a large enough population to harbor these diseases (as evidenced in the collapse of indigenous cultures when the plagues did eventually arrive), they lacked the source of human borne pathogens that would have exposed them and given them some immunity to the most devastating effects. What is the source of these pathogens? Animals. Usually domesticated ones.
Tuberculosis, smallpox, pertussis, measles and many, many more of the earth's greatest hits of diseases all started as animal-borne pathogens passed to humans. Almost certainly this happened because of agriculture and domestication putting a lot of humans and animals in close proximity. As Civilization developed in the old world, so did it's diseases. Especially dangerous were diseases that local populations hadn't been exposed to. Unlike the North America and South America, there were no shortage of domestic animals to serve as disease reservoirs. Almost as if to compensate for the variety, Europe, Africa and Asia had extensive trade and migration which in turn brought rats and fleas carrying each others diseases.
Even with a deadly disease and the presence of a vector, all of that doesn't garuntee a deadly outbreak. Yersina Pestis, the bacteria that causes Plague has existed within human society for millennia, but hasn't always been a constant killer. A complex web of biological, geographical, and cultural factors can play a role in the difference between a handful of people getting sick, and 9/10ths of your population dying. Even in relatively urban environments, it could take centuries for the exact right conditions for a deadly epidemic to come about.
It might be helpful to consider the timescale of some of new world epidemics. While some outbreaks, like the Cocoliztli epidemics (caused by Salmonella) happened almost immediately with Spanish contact in Mexico, it took centuries for Smallpox to work its way into the Plains tribes, leading the the epidemics of the late 1700s and early 1800s where millions would die from it.
So, the answer as to why the Philippines didn't suffer immediate outbreaks with Magellan (they would suffer from smallpox in the 1800s) is a combination of getting lucky with their particular arrangement of factors, and partial exposure to disease.
They key, in my personal opinion, is that they weren't so remote compared to the Americas. They had far more exposure to European, Asian, and African animal vectors. There was at least some immunity within the population, unlike North American people. Long before rats bearing the plague reached the Americas (which happened as late as the 19th century), plague could be found all over eastern Asia, and even today is home to several disease reservoirs. Japan suffered a smallpox outbreak in the 8th century. The Philippines would have been exposed to much of what Magellan could bring long before he arrived via trade with India and other areas. Exposure and immunity don't prevent an outbreak, but it does seem to make one a little less pathologically likely.
We cannot really prove a negative, and it's often very hard to say why something didn't happen, but at least we can point to a few pathological factors that effect the likelihood, and we can compared and contrast to other cultures.