Does Emrakul, the Promised End trigger if the player casting it is being controlled?
Emrakul's ability will work as normal when cast by a player controlled by another player.
When a player (A) is controlling another player (B), player A makes all of the game decisions for player B, but player B is still the one taking those actions. This is stated in a different way in rule 716.3:

Only control of the player changes. All objects are controlled by their normal controllers. A player who’s being controlled during their turn is still the active player.