We have this problem as well.
Our web app supports “Sign in with Twitter”, but when the user views our site as a direct link clicked in the Twitter iOS app, the user is switched from the Twitter app’s embedded web view to Safari in the middle of the OAuth flow and cookies that we need through that flow are lost.
Its very frustrating that “Sign in with Twitter” seems to be broken when a user follows a link in a tweet in the iOS app!
We’d like a way to either (a) break out of the embedded browser and go to Safari sooner or (b) ideally have this be a seamless experience inside the iOS twitter app itself.