My guess is that you two really do NOT have *unique* mailboxes.  Some of
the cheapy ISPs provide multiple aliases but they all point to the same
mailbox.  You need to ensure that your mailboxes are separate.  My ISP
lets me define up to 7 e-mail accounts and each gets its own physically
separate mailbox.  Some don't do that and instead you get a "family
mailbox" that is shared by multiple aliases.  That means anyone doing
something in their mailbox can affect other users of that shared
mailbox.  In some sharing scenarios, the ISP will attempt to deliver
e-mails in the shared mailbox based on which account was used to login
to that shared mailbox so only those messages with the matching e-mail
account get delivered in a mail poll, but it is still a shared mailbox.

As a test, define one account to go to your ISP's e-mail service and
define a 2nd account to retrieve e-mails from a completely different
domain, like a freebie e-mail provider that includes POP3 access.  Then
you can be sure that you are accessing two completely seperate
mailboxes.