As far as I know the extension logs you into the tool without giving you the password. The provider keeps the real paid account logged in and the extension puts that login session the cookies into your browser. that is why you open the tool and you are already inside. It also lets them hide pages like account settings or password change, so users can’t lock each other out.
One important thing. these extensions can usually read and change data on the sites you install so I would prefer a separate browser profile for them not the main one with your other logins.