First, read this post which explains the situation:
http://www.fsdreamteam.com/forum/index.php/topic,16084.msg116708.html#msg116708And, thanks to an user, which noticed the vibration stops when one presses the default Pushback key, clearly indicating PMDG DOES detect the default pushback to stop THEIR thing (whatever it is), but for some reason decided not to do the same kind of detection when GSX is pushing ( Aerosoft, Leonardo and FS Labs do that, of course ), we added the trick to send a Shift+P command when the GSX Pushback starts on a PMDG airplane, which seems to improve the situation a bit, because it fools PMDG into thinking a default pushback started, which seems to trigger some part of their code that stop the shaking.
That's the only thing we can do on our side.
It's still a trick, is not a "proper" handling, because having to send a default Shift-P just to stop the PMDG from fighting against the pushback, it's an hack, because the simulator IS starting a pushback, so it IS slowing moving the airplane by itself too, and this simultaneous movement sill results in "some" shaking, even if it's way less than it used to be.
The "proper" way to deal with this is to do it like FS Labs, Leonardo or Aerosoft did. The airplane really knows when GSX is pushing, and have a bypass-pin simulation enabled and even communicate to GSX the extension of their own NWS animation, so the two would work perfectly as they should, and that's of course only possible from the airplane code, and GSX already has everything required to do that.