No, you are not missing something... This is the intended behavior of the browser.
When the session is created, it exists within the running instance of the browser (firefox.exe). While one window remains open, that assigned session will remain. This behavior is not specific to firefox either.
Upon the first request, the server will generate a unique session from that requesting host. Every subsequent request from the browser is associated with that session. Not until the browser is closed will the session be terminated and a new session ID generated. In some cases, the session will remain active for a period even after the browser is closed. This is governed by the php application requesting and processing the data. (think cookies storing usernames for return visits)