Each head has a "mind" of its own and controls one half of the body. They are very good at coordinating movement, but it can happen that they don't agree. This generally has non-pretty results, especially when it happens in mid-air.
They are not very intelligent, at least if you expect human intelligence from a dragon. Think a very bright bird. They are very good at imitating sounds and voices, but understand the meaning of only a couple of dozen words. He is not good at all at understanding situations. (Imagine you order him to watch your bag. Bag gets stolen. Instead of making noise or anything, Ayu-Asra follows the thief, keeping on to watch the bag.)
Sylvie raised Ayu-Asra after a botched job - She was to bring a dragon egg to a mage who wanted to turn a young dragon into an familiar, but was too slow. The dragon hatched on the way, making it impossible to perform the necessary spells. Ayu-Asra does what she tells him, as long as he understands it and is not currently distracted by something shiny, loud, moving, or something that might be edible. He understands his names, and if someone uses only one of them, the other part will not be happy.