Thanks for sharing. This is very odd and must be concerning. I have not personally seen this phenomenon during my post-processing/survey control efforts.
I take color scans using a Faro Focus S70 and use white sphere targets for registration and alignments. I switch from RGB to INTENSITY often when post-processing. This is because I move my white sphere targets during the "color capturing" (RGB) period of scanning to save field time. If I viewed my targets in RGB mode then they do not display.
I recommend you try the same scan test using a checkerboard target to see if your survey points "shift" when displayed from RGB to INTENSITY. Do both control point methods selecting points and then targets to see if the problem goes away or repeats only for the point selection. If the problem repeats for points only, but not targets, then RECAP is the issue.
I hope this feedback is helpful,