I think we are now talking about different bugs. I have now solved the bug that I reported originally -- the tray icon showing up, but no menu. It can be fixed by installing the gir1.2-gtk-3.0 package. (This is on Debian testing, python3-udiskie. I have not tested with python-udiskie.)
I suggest making gir1.2-gtk-3.0 a dependency of python3-udiskie. Cheers, Greg