Yes, essentially when someone clicks on “Log In” in X app, you should be redirected to Universal Login. When you redirect, you also pass the Client ID of the Application the user is authenticating to (see the auth0 JS libraries). When the user is redirected, if they’re not logged in they will be shown a form to log in. Based on the Client ID, that is where they will be redirected after a successful login. If they are logged in, they will just be sent back to the callback URL.
I hope this helps.