Thanks for the private message. We also continued investigating after your last post and found that there is definitely something on your site/server that is enabling browser caching. That is the problem as the user's browser will cache the contents of a page. Then, even if you login, the browser is instructed to show its cached version of the page, which will be the view saved when the user was not logged in. Navigating to other pages (that haven't been cached) or telling the browser to reload will show the proper logged-in view.
Using Chrome's developer tools, you can see the browser caching is enabled in this view:
There's a line where JFBConnect's authentication process occurs. The next line is reloading the page. On the right, you can see where it says "From Disk Cache", which is the problem. Browser caching can have a dramatic impact on speed (since requests don't have to go to your server), but are not recommended whenever a page's content can change (like showing logged in vs not logged in).
We looked through the admin area of your site for caching plugins or options, but couldn't find what could be enabling browser caching. You have over 300 plugins enabled and many components, so it's difficult for us to narrow in on all the options. Additionally, your .htaccess file or other web server configuration settings could enable browser caching, which we don't have visibility into.
Hopefully, the above explanation helps you investigate and find what is enabling browser caching for your site so that you can disable it.