I have additional shared mailboxes added to Outlook 2010. These are added by the Outlook autodiscover function. The mailboxes are stored on Office 365 and I have Full Access rights.
Unfortunately, when expanding some of the mailboxes in Outlook, what I see is the contents of the mailbox for my account rather than the contents of that mailbox.
I'm an admin on our Office 365 tenancy, so I have been able to remove the rights which results in the mailbox being removed from Outlook. But when I add the access rights back, the mailbox continues to display the contents of my own mailbox.