Sea zones themselves aren’t controlled by anyone - only the convoy routes or centers within them are. You have to move into the sea zone containing a convoy route or center with a warship (not a transport) during combat movement in order to take control of it. The sea zones adjacent to it have no bearing on control of the convoy route or center.
As Mot suggested, the “adjacent” space you’re referring to is probably the fact that in order to get income from a land territory or island, you must control both it and the associated convoy route that is adjacent to it, if any (unless you’re China).