Monsters Summoned from the Extra Deck must be placed in either an Extra Monster Zone or a Main Monster Zone a Link Monsterpoints to. If control of a monster in an Extra Monster Zone changes or if that monster temporarily leaves the field, it must be placed in a Main Monster Zone when it returns, regardless if control of that monster returns to its owner.
While an Extra Monster Zone is unoccupied or when a monster is about to be Summoned to that Extra Monster Zone, that zone is not treated as being part of either player's field. While a player controls a monster in an Extra Monster Zone, that zone is considered to be part of that player's field. If a player already controls a monster in one Extra Monster Zone, they cannot Summon a monster in the other Extra Monster Zone unless there is an Extra Link to the other Extra Monster Zone.
However, even if the opponent controls both Extra Monster Zones due to an Extra Link, this does not prevent the player from Special Summoning to an Extra Monster Zone by using a monster in one of the Extra Monster Zones as Material (e.g. Special Summoning "Chimeratech Fortress Dragon" using an opponent's Machine-Type Link Monster in the Extra Monster Zone as a Fusion Material).