Who is "You" when the creature controller is not the owner?
"You" always refers to the controller of the ability, which is the controller of the creature at the time the ability triggers. So in this case, the player who controls Firedrinker Satyr at the time the damage is dealt to it - your opponent - will have the Satyr deal damage to them.


  109.5. The words "you" and "your" on an object refer to the object's controller, its would-be controller (if a player is attempting to play, cast, or activate it), or its owner (if it has no controller). For a static ability, this is the current controller of the object it's on. For an activated ability, this is the player who activated the ability. For a triggered ability, this is the controller of the object when the ability triggered, unless it's a delayed triggered ability. To determine the controller of a delayed triggered ability, see rules 603.7d-f.


from the comprehensive rules (or HTML version).