The custom pushback, exactly like the normal editor, needs to set the airplane in slew mode momentarily, otherwise it couldn't get access to the slew keys which are used for moving the pointers. Some airplanes don't react in the same way if they are momentarily placed in Slew mode, but of course that's how GSX always worked, in the normal pushback editor.
In the next update, we'll add a function to "reuse" the latest quick pushback made at that gate without having to redo it again that, in addition to speed up the procedure if you don't change the path each time, might be useful if you don't like seeing that bump with some airplanes.
and doesn't complete the push.
This shouldn't happen, unless you have another problem, and is the airplane slewing away because of one of your joystick not properly calibrated, and such a sudden movement will result in GSX aborting every procedure, because it assumed you slewed away intentionally. This can be prevented by calibrating all your joystick correctly, or remove all joystick axes from Slew mode in the Controls settings of the sim.