Even after the moderator starts the meeting, the users in the Mobile App are not shown the "Join Session" button. If I don't use that setting in the BBB activity, then they can join the session without an issue.

To test it, just create a BBB activity in your course and check the "Wait for moderator" setting. Then have the student try to join the meeting before the moderator. They will be told "waiting for moderator." Then start the meeting as the moderator. The student won't be told the meeting has started.

Even clearing the mobile cache, uninstalling the app... doesn't show the meeting has been started.

NOTE: In the browser, it works fine although I have to refresh the page in order to see the meeting is ready.