There aren’t any rules that simulate fighters landing and taking off from carriers; there’s no such thing in Axis & Allies as having one fighter “in the air” and another fighter “on the runway.”
It’s simpler than that: fighters can move over both land and sea zones. If a fighter is in a sea zone at the end of the turn, and there aren’t enough carriers to support it, then the fighter is dead. Otherwise, fighters hang out in sea zones just like any other sea-capable unit.
So, yeah, you don’t have to worry about what the setup charts say; there’s no subtle opportunity created by having fighters ‘off’ their carrier. There’s just fighters that start on land and fighters that start at sea.