Parson can also move between city zones when it is not his turn, as his side is in control of GK.
It seems to me that a flying unit is automatically in the airspace zone as long as it is not on the ground, and such can be attacked by other fliers (or by archers) regardless of whose turn it is. On its turn, a flier can choose to engage units on the walls or in the tower but is still considered to be in the airspace unless it lands.
I'm not entirely clear on the rules governing melee vs. ranged weapons in this situation, but it makes sense that a flying unit with ranged attacks could engage melee units on the walls with impunity, only being subject to ranged fire (archers) in return, but a melee unit like Ansom has to get close enough to be vulnerable to counterattack.
As an aside, I love how strong the underlying world mechanics are in this comic. Besides creating a great deal of food for debate, this contributes to suspension of disbelief by allowing the story to proceed without tripping over logical inconsistencies.