When accessing Outlook Web Access other users mailbox's open without prompting username/passwords

The problem I'm having is that when I log in to any of the spare notebook pc's in our org and try to access Outlook Web Access it automatically opens someone elses mailbox without even prompting for a username and password. Now, I have to mention that all these notbooks use the same shared domain account created for this purpous.  

I also need to mention that despite the use of a secure certificate I also get the following access results::

(When inside the network) using "http" in the browser allows access to OWA too instead of access allowed only using "https" and browser proceeds to open users mailbox without prompting.

(When outside the network) again, both "http" and "https" work and I do get prompted for a username and password thus opening the correct mailbox.

Would anyone know or can help me troubleshoot why other users mailboxes open without prompting me for username and password when accessing OWA internally?

Thanks in advance,
Evan