Log out doesn't log out : spy account, read mails, see OneDrive's file in another account than yours

That's sort of known/expected behavior, simply clicking the Log out button never does a "full" logout as there's a lot of caching happening on both the client and the server side. Closing the browser window should generally work, but only if you close any other currently opened tabs/windows, *and* also make sure to close any background processes via task manager. And you also have to take into effect the KMSI setting and the authentication method used by your organization (anything configured for Windows Integrated Authentication will just log you in directly with current users' credentials).

Anyway, these forums are not a support channel, if you want to submit this as a bug open a support case.