First, make sure to clear all saved logins. You can do that here:

(WIN) orange Firefox button (or Tools menu) > Options > Security > "Saved Passwords"

Second, if the "Remember passwords" checkbox get checked by itself when you exit and restart Firefox, check for a user.js file as described in this article: How to fix preferences that won't save. (If viewing/printing on Mac, use the OS selector above the article to change to Windows to get the correct menus/button labels.)

So, I had already checked the saved passwords, and there are none for either of those sites - never have been. And I did not check it by mistake since I never want to remember those on that computer nor have those sites on the exception list (don't want a list of websites there). I will check that link though once I can get back to that computer. Thanks.

Just a note about cookies: some cookie-based logins that normally expire at the end of a session may remain "live" if Firefox resumes/restores your earlier session.

Sorry - I accidentally chose your answer as the solution, when I don't think it is. While what you say makes sense, I never had this problem with older versions. Once you restart Firefox, it is supposed to start a new session, even if you open the previous tabs from the last one. That is what is going wrong in this version. I should be able to restart FF, and it start a new session with previous tabs, but maybe it is not starting a new session.

There is a way to modify the session restore feature to dump the cookies. This is linked to other form data.

(1) In a new tab, type or paste about:config in the address bar and press Enter. Click the button promising to be careful.

(2) In the search box that appears above the list, type or paste sess and pause while the list is filtered

(3) Double-click the following preferences and set them to the desired value for private data (site cookies, form data, POST data, and scrollbar position on the page):

(A) browser.sessionstore.privacy_level - applies to resuming your session automatically (e.g., after updating) or if you set Firefox start up to "Show my windows and tabs from last time"

• Save/restore for both HTTP and HTTPS sites => 0 (default)
• Save/restore for HTTP sites only => 1
• Do not save/restore for any sites => 2

(B) browser.sessionstore.privacy_level_deferred - applies to ad hoc session restore from the user interface (i.e., any time you are not automatically restoring your previous session)

• Save/restore for both HTTP and HTTPS sites => 0
• Save/restore for HTTP sites only => 1 (default)
• Do not save/restore for any sites => 2

Source of this tip: firefox is remembering passwords i tell it not to. browser reopens after computer restart and i can still login. it's really annoying.

Thanks. Back in the office and adjusting those privacy settings (which had gone back to default since the update) seems to have fixed the problem.