Google API Browser based Authentication

I'm developing a web app that will need user providing permission to access their Gmail data. It works well in my local where a browser opens up for granting permission. When I run it in PA, it is saying 'A Browser has been Opened to visit Image

does this happen when you get their password and try to sign in for them?

No.. I cannot get their password and sign in. I want this URL to be opened up at the user's browser. When I try in local, as both server and client are my laptop, the browser is getting opened fine (browser is opening from server functionality). But I'm not sure how to make this work from PA.

You need to use a different way of getting permissions. The method you're using is for providing permissions to software that your user is running on their machine. You need to use this form of authentication: it sends the user to a google URL and then, once they've granted permissions, it redirects back to your app.