Login UX on Android and other platforms

I am build a native integration of OI Calendar for Android and Afari has also a native app.

There current solution is not ideal (- we use CustomTabs). The design goal was that it looks like as if the authentication happens within the application (and not in the browser - this has same disadvantages for the login flow UX but that is a different issue ).

Would it make more sense to educate the user that the Blockstack Browser does the authentication (and not the app)? And provide some UI that the authentication is starting now in the blockstack browser?
On the web there is a similar tension between redirecting to browser.blockstack.org (ideally in the same tab) and to using the locally installed browser.

What was the intention to name the Blockstack Browser like that and not call it authenticator or identity manager?