I tried to reproduce your problem, but I can’t manage it in either the current Mac or iPad version. Could you please upload a screenshot of the relevant Perspective options/settings?
Additionally: In my perspectives, I notice that the appearance of projects (collapsed or expanded projects) is remembered in the last used state when switching perspectives and appears the same when accessed again as it did when exiting. Even when Omnifocus is shut down, the state is saved and when restarting, tasks and projects appear as before in terms of display.