The sniper would need to fire the rifle several second BEFORE the duelers fired for the bullet to arrive on target when they fired. It can take several seconds for the bullet to travel a mile. The sniper would need to know precisely how long after the "aim" order the "fire" order would come.
Sound travels at about 1,100 feet per second at sea level so it takes just under 5 seconds to travel one mile. If the sniper shot at the same time as the pistol shot, the sound would be heard almost 5 seconds later.
The actual Hamilton-Burr duel occurred in Weehawken, N.J. not on Governor's Island. Weehawken lies directly across from Manhattan, and for Manhattanites, a trip to there would be more convenient than Governor's Island, which can only be reached by boat.
Captain Danny Ross says that the shot came from across the East River. Considering that the duel reenactment (and filming) was on Governors Island, this would be incorrect. The southern tidal waters of the East River (which is not actually a river) flow between Manhattan and Brooklyn. Therefore a shot across the river from Lower Manhattan would go across to Brooklyn, not Governors Island.