Hi Friggs,
I know this is an old thread, but I am renting the 200-500 for the weekend and noticed that it does exactly what you describe here. (I found this thread doing a Google search 'Nikon 200-500 single point jump') I am using it with a D500. I rented the 200-500 and the Tamron 150-600 G2 to compare them over the next couple days. I popped each lens on the camera briefly while at the camera shop to see how they performed.
The camera was in Shutter priority @ 1/1600, VR on, back button focus, AF-C, single point focus (center). The Nikon and the Tamron both did the typical slight jump when VR was activated. But when using the 200-500 the focus point did a noticable jump AFTER every shot. Tried using both sport and normal VR setting, with the same result. I had the counter guy try it, and he experienced the same thing. Said he'd never seen it before in any lens (neither have I). When checking the focus point in playback mode, it moved around the subject, just as it appeared to be doing while shooting.
When I got home with the lenses I continued to shoot around a bit with both lenses, with the same result regarding the jumping focus point.
I've been shooting since the 70's, digital since 2000, and have used a D300 for the last 7-8 years. I've owned and used VR lenses (18-200, 70-300, 70-200), and none have done this.
I will continue to see how the lens does in this regard over the weekend, but it's not a good sign.
Have you figured out this issue?