Yes, you do. You control a zone only if you have at least one land unit in it and the enemy has no land units in it. A zone that has no land units in it is controlled by no one (bottom of page 10).
To further clarify, all submerged subs resurface near the end of each player’s turn in Phase 8 - Submerged Submarines Resurface/Damaged Battleships Uprighted. In effect, no submarine is considered submerged at the beginning of any given player’s turn. This means that a sub that escaped combat by submerging may be attacked again on the next player’s turn (assuming that player is an enemy) and would have to submerge again in order to escape combat. It also means that it is free to do whatever it wants on its owner’s turn, as Saburo pointed out.
