One of the biggest problems traveling in Southeast Asia is the burning season that affects Malaysia, Indonesia, Singapore, and Thailand. This is when crops in the countryside are burned in open air to clear the land for the next planting season, which causes severe air pollution and bad haze in the cities.
In Thailand this happens from February-April. In Indonesia this happens from June through October. The Indonesian burning causes a lot of issues for surrounding countries like Malaysia and Singapore
In the Philippines, we are not as affected by this phenomenon as other Southeast Asian countries
Air quality in the Philippines is fairly constant throughout the year, but it will get a little worse sometime between June and October due to the Indonesian haze drifting over, but it's not too bad that entire cities get blanketed by the pollution.
So if you're planning a trip to the Philippines, burning season should not be a big factor in determining the timing of your visit. The air outside of Manila and other major cities like Cebu will generally be great any time of the year