I think you are in error, Switch.
For one, it’s MUCH easier to assume that a nation’s fighters are on their own carrier instead of just trying to remember who landed what on what carrier 15 rounds ago.
Secondly, I think Tim is correct, fighters are assumed to have been launched each turn and land at the end of the turn to refuel. They cannot move to a new territory, but the same sea zone is not a different territory.
Third, as mentioned before, Carriers do not count as a territory, otherwise launching from a carrier would be the same as leaving an island chain, it is not.
Fourth, just from a historical and logical precedent, we know that carrier air groups flew cover air patrol when not actively attacking the enemy, therefore it would be logical sense for them to land on their own carriers to refuel and change crews whenever possible.
Lastly, when you attack a fleet with more than one carrier, you do not kill the fighters that were originally on that carrier when you sink a carrier, the defending fighters only die at the end of combat if there is no viable landing spot. Therefore, we do have a game precedent set to support the idea that fighters can be on whatever carrier the owner choses whenever the owner choses them to be there, regardless of whose turn it is, provided there is room for the fighters on carriers present.