Does the worshipper say "Allahu Akbar" before the sitting of rest (upon rising from prostration) or after it (when rising for the next unit of prayer)? And how should the Imam act towards someone who does not observe the sitting of rest if the Imam has said "Allahu Akbar" before it?

The session of rest (jalsat al-istirahah) is a Sunnah (definition). The more preponderant opinion is that when a worshipper performs the second prostration, he raises himself, saying "Allahu Akbar," then sits for the session of rest. After that, he stands up without saying "Allahu Akbar." As for the Imam, if he fears that the matter might be confusing to the congregants or that they might rush ahead, he should sit for the session of rest without saying "Allahu Akbar," and then say "Allahu Akbar" when he rises to a standing position.