There's not much we can do to fix this from our side, because what you are looking at, is some kind of custom ground simulation that keeps running in the PMDG, which it's not turned off when GSX send the standard Simconnect command to "freeze" the airplane, which every other airplane responds to, and even those that have a custom ground modeling, like the FS Labs A320, have been programmed to temporarily pause their simulator while GSX is pushing.
PMDG DOES seem to recognize the standard pushback so, when you are using the NGXu, we send a Shift+P command at the start of our pushback, to fool the NGXu into thinking a default pushback started. This reduces a lot the vibration compared to what it used to be, but it won't fix it entirely, because now GSX would have to fight against the default Pushback instead against the PMDG simulation, so it's still not perfect, but it's better than it used to be.
You can even control if GSX does this or not for any airplane, with the "Pushback Dummy event" in the GSX Airplane configuration page.
So, we did all what we could to reduce this problem, but the real solution would be that PMDG would recognize the standard Simconnect "Freeze" event (like any other airplane), and paused their own custom ground handling while the airplane is in a frozen state, and this would completely solve every problem, without requiring the dummy pushback trick.