In my opinion, the behavior of flying units is fine, but archers should be less likely to fire at routed enemies if there are friendly troops near them. Hold your fire and get closer instead.
If the flying units are getting killed in melee by cut off routing enemies... you need some tougher flyers.
But in my experience the main threat in this situation is the archers/crossbowmen continuing to fire at the routing units and hitting their pursuers instead.