James,
That's obviously not good, or right. Do you have caching enabled on your Joomla site? We do a lot to work around caching those values, but that's about the best thing I can think of is that the page was rendered for "Jorge" and then that is what's being displayed to the next user. If caching is enabled, please try to disable it (even temporarily) and test again.
On a side note, I just used the Login with Facebook button on your site and the greeting properly said "Welcome Alex!". Let me know if it says Alex, Jorge, or something else for you.
We'll help you get to the bottom of it one way or another. This isn't a widespread issue though (we'd hear a lot about it if it were), so we just need to understand what's happening differently on your site.
Thanks,
Alex