Mark is correct, one trigger pull per barrel is required or the firearm is usually considered an NFA machine gun. However, the ATF has given some companies exemptions, such as the ridiculous Arsenal double barrel 1911 pistol. It fires both barrels with the single pull of the trigger and is not considered an NFA firearm by ATF.
Pulling the rear trigger first on a double barrel shotgun and firing both barrels is not a design that most hunters or shooters wish for. I've fixed a good number of doubles that were, well, doubling from poor sear and hammer contact/shape and tension. It's not the worst recoil in the world but it is unpleasant. I'm guessing their marketing department didn't hire the best translator.
