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Sorry, Duane, that's not true.
I just tested it with FF and the exact same thing happens with multiple tabs in a private window as well as multiple private windows. That means session information is still shared among multiple private tabs and even multiple private windows. That also means you should not force a logon for a different user in another tab or second window because it risks corrupting the entire session in an unpredictable manner.
Having said all that and having checked FF docs which indicate session information is compartmentalized between primary and private windows, I tested with a regular FF window logged into GIO as "Member A" and then opened a separate private window addressed to GIO and it clearly showed it was not automatically authenticated as Member A. So, in that singular scenario, it would appear to create two isolated sessions correctly. I still wouldn't recommend it, though.
I contend it is far easier and far more reliable to use an alternate browser for concrete session isolation.