Ramp personnel reported the aircraft stopped in the correction position while being marshalled to the gate; but then started rolling again while a gate agent was placing nose chocks. Captain then set parking brake.

Narrative

Aircraft X was pulling into Gate XX at ZZZ. I was wingwalking the left side of the plane. Crew chief made the X sign with her wands and the aircraft stopped on its mark; but then; inexplicably; began rolling again; despite the crew chief holding the X sign. Another gate agent placing the nose chocks had to quickly get out of the way of the nosegear to avoid injury. The jetbridge stayed away from the aircraft.The aircraft finally stopped on the wrong line; and a short time later was pushed back to its correct mark.Crew chief spoke to pilot while pushing aircraft back to its correct mark; and pilot stated that he 'didn't know he did not set the [parking] brake;' which explains why the aircraft started rolling again after the pilot released the foot brakes.As the jetbridge waited; the crew chief who held up the X sign pushed back the aircraft to the correct mark; while communicating with the pilot about the incident.Pilots should maintain situational awareness at all times; including while parking at the gate; to avoid needless injury to ground staff; and delays for both passengers and American's operation as a whole at the station.