Correct me if I'm wrong, but I think what you're asking is why when you redirect the user to the auth page, they get prompted to "allow" the app even though they already have.
This app is using OAuth 1. Dropbox does do auto redirection for OAuth 2 if the user has already authorized the app. So if you use OAuth 2 instead, a user who has already authorized your app will be forwarded directly back to the app instead of being asked to click the Allow button first.