THE FLIGHT HAD ARRIVED AT THE JETWAY AND THE PASSENGERS WERE BEGINNING TO DEPLANE. BEFORE EXTERNAL GROUND POWER WAS SUPPLIED TO THE AIRPLANE, THE CAPT PREMATURELY SHUT DOWN THE NUMBER ONE ENGINE WHICH WAS SUPPLYING ELECTRICAL POWER TO THE CABIN. WHEN THE ENGINE WAS SHUT DOWN, THE MAIN CABIN LIGHTS WENT OUT, FOLLOWED IMMEDIATELY BY THE ILLUMINATION OF THE BATTERY-POWERED EMERGENCY FLOOR LIGHTS. THE FLIGHT ENGINEER ANNOUNCED TO THE CAPT THAT HE WAS STARTING THE AUXILIARY POWER UNIT (APU). AS HE STARTED THE APU, AN EXHAUST FLAME MOMENTARILY CAME OUT FROM THE APU EXHAUST PIPE LOCATED NEAR THE TOP OF THE RIGHT WING ROOT. SOME PASSENGERS YELLED 'FIRE' AND BEGAN AN UNCOMMANDED EVACUATION THROUGH THE OVERWING EXITS. CREW MEMBERS WERE ABLE TO STOP THE EVAUCATION, BUT NOT BEFORE SEVERAL PASSENGERS HAD JUMPED OFF THE WINGS AND INCURRED INJURIES.