I believe you might be conflating being logged in with a user authorizing your Twitter app to make requests on behalf of them.
It would be worthwhile to explain the difference between the authorize and authenticate endpoints:
If you use the authorize endpoint with your implementation of the sign in with Twitter process, the user will have to log in to Twitter every time you want to make a request on behalf of them.
If you use the authenticate endpoint with your implementation of the sign in with Twitter process, the redirect will occur without the user having to re-approve the application as long as that user is logged in to Twitter.
We do not have an endpoint to log users out of Twitter. We do, however, have an endpoint that you can use invalidate users’ request tokens.