After the pushback was done, the plane moves forward on it own before it was says Set parking breaks.
If you turned on your engine while GSX was pushing, and you have a bit of power, or your airplane flight model is made in a way that it can start to move even with no throttles, it's normal it would move, and of course this doesn't have anything to do with GSX, because it would happen in any case.
Perhaps you just have your joystick axes not properly calibrated, or the null zone for the throttle axis not calibrated, so you are applying power as soon as the engine started, without realizing it.
Again, not a GSX problem, and nobody ever reported such issue before.
Unless, as I've said, you use the Dash 8, in this case it's to be expected and, again, it's not a GSX problem either, because that airplane doesn't respond to the standard simulation freeze command, so it's up to Majestic to add such control to have their own custom flight model react to that or, as an alternative, use the variable we added to GSX, to allow 3rd party developers that have custom flight models, to know when to freeze their simulation because GSX it's pushing.