how to avoid page caching on authentication? And CI session or PHP's $_SESSION ?

[eluser]moonbeetle[/eluser]
I ran into a problem and I suspect an internal web server serving cached pages to be the root of all evil.

When user "Bob" logs in, he gets a greeting "Welcome Bob!".
When user "Jane" logs in a few minutes later, she gets a greeting "Welcome Bob!".
Both Bob and Jane work at the same company (where Internet access is likely to be monitored), though their login credentials are different.

CI session is used (the session ID is stored in the cookie, the rest of the session data in the database). Apart from my particular problem which might not have anything to do with CI, I was wondering if replacing CI sessions with PHP's $_SESSION[] might be an improvement?