Actually, if you replicated the steps on any Unix/Linux box, I'd expect to see exactly the same thing happen.
I don't think so. Since each user has a separate home directory, typically /home/$user that is created with permissions of 700, users wouldn't have access to the same profile unless they were logged in as root (which is really dumb- many programs explicitly tell you how dumb an idea this is when you start them).
Even if you had installed the profile under a shared user, when you attempted to start FF as another user, it would create the new profile under your home directory unless you'd explicitly modified the start script or your environment. Granted, this is possible, but I don't see the purpose of having $MOZILLA_FIVE_HOME be a shared directory.
One of life's greatest pleasures is having a spouse from whom you don't feel the need to keep secrets.