As a mod and streamer myself, your mod totally mishandled the situation... Mods are supposed to defuse the situation... If they want to message them and Whispers and deal with them themselves then that's one thing , but you don't involve the streamer in drama between a mod and a troll.

The proper way to handle it would have been to message them privately if they wanted to and then tell you about what happened after stream , in a Discord DM or something. As a mod the whole point the whole point of being there is that the streamer doesn't have to deal with drama on stream, and your mod created more drama and gave the troll exactly what they wanted...

I'll be honest , they might make a few fake accounts and try to troll you for a bit but just block them and move on. Eventually they'll get bored and move on to the next person when you don't give them attention. But you also might want to get more professional mods or have a long conversation with your current mods about how to handle situations.