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от Philip Alexander Янв. 12, 2017 ·

But all of the private tabs share the same session and the same cookie jar. Therefore, you can't connect from two different private tabs to the same website twice using different login credentials.

Это отзыв для предыдущей версии этого дополнения (0.2.0). 

от Infocatcher (Разработчик) на Янв. 12, 2017 ·

This is depends on Firefox implementation of private browsing: built-in private windows also share the same cookies and other things.
Also you can try Multifox: https://addons.mozilla.org/firefox/addon/multifox/