If you want a "Shut down Opus" option on the File menu then you can put one there yourself. Almost all of the menus in Opus are editable.
You can also set Opus to automatically shutdown when the last window is closed, if you want that.
See How to Exit Directory Opus in the FAQs.
Having exited Opus manually and confirmed that it restarts with something other than My Computer, what happens if you reboot now?
If you still get My Computer then it suggests the problem isn't at shutdown but at startup. Maybe Opus is launching before the folders you had it pointed to are available?