Normally, you should not see any insects in your system.
But, insects (small bugs, flies) can enter the system and be a pest (of course!). If this happens, more than likely they have entered through the peat (or soil, etc.) that you are adding to the system. Once they get in they multiply fast!
So what do you do? The solution is pretty easy. Immediately add diatomaceous earth to your system. Diatomaceous earth is a natural bug killer. Sprinkle it over the mass. This should eradicate the bugs!
To control them on an on-going basis, try mixing some DE into your regular daily additive (i.e., your peat moss, etc.).