You kept on using the site in the same tab? Usually a site maintains the continuity of your session by setting one or more cookies. Firefox returns those cookies with each new request to the site so it will recognize your browser as being the same one that was there a moment before. If you didn't close Firefox or switch from a regular to a private window, then I think Firefox will keep sending those same cookies even if you switch from one network to another.

Note: if you are trying to take actions that require being logged in, you can't completely block cookies. However, you can manage them in various ways to limit how long Firefox keeps them.

I will try it again at some point, I was sure I closed that window and opened another, I didn't close Firefox completely, I will also see what I can do about limiting the time cookies are kept, Thanks

Sites typically set long-lived cookies. You can set Firefox to dump cookies after each session, and then when you find that annoying on some some sites, create exceptions for those sites so they can set persistent cookies.

This is set on the Options page, Privacy & Security panel. This is the key area:

Thanks for the help