When he flys up onto that tower and chills there, is that my que to leave? Online version.
Nope. It let's you know when he's left (accessing server). Depending on what you're doing and where, he'll 'roost' up there sometimes. Eventually, he'll come back down. Fight him on the other end of the arena so he doesn't fly up there.
He flies away completely in 8mins (I think) unless you take him down faster or die.