I can reproduce the symptom, actually a more violent one, in about 10~15 minutes.

What I do is first turn the ignition off and pull the key out. Wait for 10~15 minutes, during which time I do not do anything like opening the door or windows, I just stay put. While waiting, I can hear what sounds like HVAC deactivating and then about 10 minutes later I can hear another electric noise which I suppose is some module go sleeping mode.

About 5 minutes after that when I turn the ignition on without giving the system any time to wake up at all, the rpm needle goes crazy moving up and down around 500rpm and the engine vibrates violently causing the whole chassis to move about!