Rated 3 out of 5 stars

by Philip Alexander on Jan. 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.

This review is for a previous version of the add-on (0.2.0). 

by Infocatcher (Developer) on Jan. 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/