At check-in (and possibly the boarding gate) you'll need to present the Philippine passport to prove you'll be able to enter the country. At immigration exiting the U.A.E. (if there is) you'll need to show the Indian passport with the visa to prove you were staying legally -- they shouldn't care where you're going, just that you had a visa to be in the U.A.E. and haven't overstayed.
At Philippines immigration present the Philippine passport, similarly they don't care where you've been and just want to make sure you're allow to enter the Philippines.
On the return leg reverse it depending where you're going, show the passport that proves you can enter your destination at check-in, show the Philippine passport at Philippine exit clearance, etc.
Be ready, in case anyone asks, to show the other passport and explain what you've done. But in most cases each person that looks at your passport is trying to confirm a specific thing and you just need to show the passport that proves that.