It's possible that Container extensions -- which create a separate context from regular and private windows -- do not work / work differently in private windows. I haven't tested! But here are my general comments:

Extensions don't work in private windows automatically. When you install an extension, usually there is a confirmation dialog panel near the menu button with a checkbox to enable the extension in private windows above the large OK button. To change that after installation, you can

(1) Open the Add-ons page. Either:

• Ctrl+Shift+a (Mac: Command+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons
• type or paste about:addons in the address bar and press Enter/Return

(2) In the left column of the Add-ons page, click Extensions.

On the right side, each extension allowed to run in private windows will have a purple mask icon next to its name. To change that permission, click the extension's name to reveal its Details panel, and scroll down to the controls area where you can select what you prefer:

Run in Private Windows (*) Allow ( ) Don’t Allow

Repeat with other extensions as needed.

Does that behave the way you expect?

I followed your steps up until: "Run in Private Windows (*) Allow ( ) Don’t Allow "

where I find: "Not Allowed in Private Windows This extension does not run while private browsing. Learn more" where the learn more link takes me to: https://support.mozilla.org/en-US/kb/extensions-private-browsing?as=u&utm_source=inproduct

So I guess that when I logged in to that site I was logged in through Facebook and didn't know it. Damn!

Any site where you sign in using your Facebook account gets access to some of your FB profile information. Usually they disclose what they are accessing the first time you sign in. Each person needs to make their own judgment about the value of the services and their information. And we're all a little nervous that FB may slip up and share more than we know about.

Containers do not work in Private Browsing mode.

• https://support.mozilla.org/en-US/kb/containers

Note that Containers is disabled in Private Browsing and when Never Remember History is selected in your privacy preferences.