Question: Sometimes people in masjids offer qaḍā’ prayers in congregation, and the imam of the congregation also offers qaḍā’ prayers which were surely missed or he offers as a caution, is that correct?

Answer: If the Imam says a certainly missed prayer, the believers may offer behind him a surely/possibly missed prayer.
Of course, it should be noted that the connection in congregational prayer is not achieved through someone who says qaḍā’ prayer as caution.
However, if the Imam says qaḍā’ prayer as a caution, we can say prayer behind him only if we say it as a caution and the reason for saying it as caution is the same as that of imam.