My Outlook with Office 2013 and 2010 does save the .pst file [different computers]. Having the messages on your IPS's server is convenient when accessing via a Web connection to their E-Mail page, most ISPs do it. That's the difference between an installed E-Mail Client such as Outlook, Thunderbird, the now-defunct IncrediMail, etc., and the Webmail/Online E-Mail feature using a browser. A setting int Outlook should be checked/unchecked if wanting to use different devices or traveling to assure no one computer will delete the messages from the server, assure all devices can still see them.