Your issue is, you are expecting zones to auto switch when you click on them and that's now how zones work in MC.
In MC, you have to select a zone by clicking it, then select some files and double click to play, or use the right click menus to add to playing now, or a similar action. It's totally expected for you to experience what you are reporting: You start playback in zone A, then you click on zone B and nothing changes: Zone A keeps playing and Zone B does nothing.
There are many ways you could handle this. ONE way would be to start playback in Zone A. Then Zone Link A to B. After a few seconds A and B would be playing (somewhat, but not perfectly) in sync. Then you could press stop on Zone A, which would stop playback in A, but let B continue as normal. Unfortunately, this won't let you then restart A in sync with B. You'd have to re-sync them again.
Another method for you would be to Zone Link A and B, and just play everything to A and B at the same time. You'd use the preamp or other associated equipment from the A and B sound systems to control when you hear playback from A or B. A and B will always play, but you switch between them and/or change volumes with the input selector on a preamp, or preamps (plural).
If you describe the way you want to use this for demonstration or comparison purposes, we may be able to suggest the correct methodology.
Good luck!
Brian.