If it's a server-side caching issue, then yes, a user could experience it. If the server/website/etc is storing a copy of a page as if a specific user is logged in, that may show up to other users as well.
I would check the System - Page Cache and disable it, if enabled. That will store the HTML of pages for your site and serve them up directly. If a page gets stored by Joomla when user 'a' is logged, that raw HTML will be handed to user 'b' if they visit the same page. The Page Cache plugin should only be used on sites without user authentication.
Other caching in the control panel area for System Cache can remain enabled. That acts differently.
As for our site, yeah, we had a technical snafu. Still investigating, but got it up now. Thanks for your patience
Alex