A client reported some problems with their Sign out functionality of their Office365 solution. They were using TMG as ADFS proxy and a load balancer, so I was expecting one of those components to be the root cause. Luckily I was able to quickly cut them out of the equation by using host files for name resolution. It all came down to updating the preferred authentication method for my ADFS site, from Windows Integrated to Forms based. Now it works. User can sign out and sign in with another user, without taking over any previous sessions.
So navigate to your ../ADFS/LS site physical location and open the web.config and modify the section as below. The change is on the Forms and Integrated sections switched places. Hopefully this will save you some annoyance for your Office365 implementations.
<localAuthenticationTypes> <add name="Forms" page="FormsSignIn.aspx" /> <add name="Integrated" page="auth/integrated/" /> <add name="TlsClient" page="auth/sslclient/" /> <add name="Basic" page="auth/basic/" /> </localAuthenticationTypes>
The below link describes the above for AD FS 3.0