What is required of congregants who did not hear the imam's takbir, bowing, or rising from bowing, then completed the prayer with him after seeing him prostrate?

The congregants were obligated to bow, then rise from bowing, then catch up with their Imam. Since they did not do so, they must, after the Imam's salām, perform one rak'ah to compensate for the bowing and rising from it. If they do not do this, the prayer is invalid, and they must repeat it for having omitted two of its pillars.