Sorry for all the confusion. Incognito / private tabs are created by default if the extension is allowed to run in in incognito / private mode. You can change this in the extension settings. There's now a settings button in the extension popup, even if you're logged out.
The issue that affected you had to do with timing. Web Extensions do not execute their scripts in a deterministic order. I had to install / deinstall / try / retry a few times to find out that in some cases the content script was executed too early.
With version 3.2.38 you should now be able to solve captchas, skip captchas and force incognito mode
Let me know if there are still issues.