It does sound like you are not actually successfully logging out the Firebase Auth. I use Firebase Auth, on web - and the "previous user" only shows up when they have *not* signed out (there's an active cookie in the browser). Either you are not making the correct call, or possibly not waiting for the promise to resolve.
When my users are signed out,they do have to sign in / choose account - my code does *not* prompt them with possible accounts (that would be a security link), although *Google* (when using Google as the sign-in) does remember and present the past-used logins, usually.