Typhoon Season is June to October.
You may get lucky or unlucky, have a backup plan just incase
October may have a better chance up to December
November is usually when the winds change and the weather becomes better but still cloudy

We usually do a holiday end of July, start of August here every year and you really can't predict, sometimes its good, sometimes its bad and sometimes its the worst.

Typhoon season seems to be coming later and later every year though (global warming?)
Today its hot, but it could be raining a lot in the afternoon.

Usually weather systems forming by Guam hit the Philippines, so if there's a storm or 2 over there, in a few weeks it will hit the Philippines.
http://www.goes.noaa.gov/guam/guamloops/guamir.html

As such I usually prefer to go abroad as the weather wont be Typhoon season

But Aman Pulo is on the western side of the Philippines so you will have a few days notice to see if there's a Typhoon coming in from the eastern sea and where it will likely pass.