I can't say mine continues after the movement stops, but I've never paid attention. Our plan of attack has been:
1) triangulating stabilizers (products like JT's StrongArms, UltraFab Eliminators, SteadyFast system or your own DIY) on each corner from the stabilizers to the frame (we have the UltraFabs)
2) good between the wheel chocks (we went with RotoChocks)
3) Extra jacks under the frame near the axles - we haven't done this yet, but I'm starting with the Valterra Jack Stands with extremely low expectations and will likely move to scissor jacks.
With 1 and 2, we still have movement- more than we'd prefer. I'm hoping 3 gets us closer to the "rock solid" that many people claim. At the end of the day, wheels and a suspension are part of our foundation, so I expect some movement. I just don't need to know when my 9 year old rolls over 35' feet away. And vice versa- it'd be nice if my MIL doesn't need her seasickness wristbands when she sleeps back in the bunkhouse.