To clarify, Private Browsing mode is essentially a fresh session. What I mean is that all of your data from Private Browsing will be remembered for as long as you have the Private Browsing window open. It isn't erased until you close your Private Browsing session.

For example, if you login to an account and close that tab, but continue to browse in Private Browsing mode, you will be automatically logged in when you revisit that website.

Note that on Mac this can be more complicated because you can close all open windows, but keep the application running. You would have to quit the Firefox application if you use permanent Private Browsing mode (Always use Private Browsing mode; Never Remember History) to close the current session.

Wesley Branton, I do not think that is correct. Private browsing should erase al login information when a session is completed. this is stated in web site https://support.mozilla.org/en-US/kb/private-browsing-use-firefox-without-history

Private Browsing automatically erases your browsing information, such as passwords, cookies, and history, leaving no trace after you end the session. Firefox also has Content Blocking, which prevents hidden trackers from collecting your data across multiple sites and slowing down your browsing.

I consider ending a session after I log out if 365, or Mozilla support. That session is complete. But If I open another tab it logs me in immediately on version 69 on a Mac Os x.

This is not about the session with the website in the current tab, but about the Firefox Private Browsing mode session. You need to logout properly (and you should always do this to clear the session ID stored on the server) from a website if you are done and not simply close the Tab. Firefox doesn't remove a stored password, but will clear a 'remember me' cookie if you close a Firefox PB mode session (i.e. close all PB mode windows/tabs).

I am aware it about the session in the current tab.

I have logged out of 365 which is confirmed by 365 web app then closed the tab 365 was using. When I opened another tab it immediately logged me back into 365 office and that should never of occurred in private browsing.

I have since tried it and it did not log me into 365 or mozilla support automatically after closing the tab and logging back in

I reinstalled Firefox after noticing the add-on (no script, ublock) where missing.