I respectfully disagree, beloved.
If Paul knew the man was unsaved...or only believed that he was...based on what we know of the Ambassador's heart for the lost, which would make more sense for Paul to have prescribed?
1. Kick the guy out of the congregation and hope he manages to hear the Gospel of grace and get saved while he's back in contact with no one but Christ-hating pagans?
2. Get the elders at Corinth to make sure the guy had understood and had believed the Gospel of grace, and was in fact saved (or not)?
Answer: Paul didn't do either of these. Instead, he treated the guy as if he [Paul] ASSUMED the guy was saved, though sinning grievously, and so treated him very, very harshly for his own good and the good of that stupid, carnal church that should have already dealt with him.
The turning over to Satan was, I assume, part of Paul's apostolic authority. But would Paul even need to turn over an unbeliever to Satan? No. If unsaved, the guy would already belong to the Devil.
I believe the guy was saved the whole time. That's the only way Paul's treatment of him makes any sense.
Right or wrong, let iron sharpen iron!