Was using private browsing to log in to work gmail last night and found it really creepy how it remained logged in across private tabs. Thought the whole point of a private tab was to completely isolate a browsing session, now you can never be certain your Google credentials are not being shared in these private sessions or even contaminate my non-private sessions. Going to have to use another browser for my work ses…
If you mean "Incognito mode", then that's always happened. You need to close all tabs.
Exactly the same for FireFox's private browsing.