I just tried both functions, using a default A321 from FSX, and FSDT CYVR, with default Left pushback at Gate 18A and this is the result:
- "Stop here and complete pushback" results in the plane being pushed about 4-5 meters more, enough to slow down, followed by the request to Set Parking brakes, with the Wingwalker then going close to the tow truck to unlock gear, and saying "tow truck disconnected", then "Left is clear, right is clear", the "clear to start engines" and "have a good trip", so it's just like the end of a normal pushback, but performed earlier, exactly how that function is supposed to work.
- "Abort pushback" results in the airplane stopping immediately, and the tow truck and wingwalker disappearing, exactly how that function is supposed to work.
So no, at least it's sure it doesn't happen everywhere and with every aircraft so, as usual when reporting a problem with GSX, always include ALL the complete information: the airplane used, the scenery used, the gate used, the kind of pushback chosen and everything that can be useful to know for us to TRY to replicate your situation.