Data is synced from the Chrome Web Store. View the official store page for the most current information.
To enable the extension, enter your proxy login and password in the form.
Once it's done, you should never see any proxy login popup again.
As you probably saw, Proxy Auto Auth requires the permission to "view your data" on every sites. This permission is just necessary to achieve what this extension does. But be sure that none of your data is stored or used in any way.