There can be exit immigration, but it doesn't exist unless it is setup. By the way, did they ask you for your papers, or just customs stuff?
Bottom line - call it whatever you like, but, if the U.S. requires that U.S. citizens of dual or single nationality leave the U.S. on a U.S. passport, that is the one that should be presented to the air carrier representative when checking in for an itinerary where one will be leaving the U.S.