As you guys correctly guessed, the animals each have two 'tells' - one where the animal is going to accept your food, and one where they're about to bite you.
You can't just 'poop' the fly on the ground and let them eat it, because they demand to be hand fed. Lazy fuckers.
Here's what the rest of them look like in action:
All in all not a bad way to make money, though it can't really beat the Key West part time job for cheeseability.