I don’t think there’s anything inherently wrong with them being alone together, however if you aren’t comfortable with it and you tell her that, she has a choice to make. Setting acceptable boundaries is a fundamental part of any relationship.
It would be understandable if she said “No, we’re still going to hang out. We’re just friends.”
It would also be understandable if she chose to cancel or to invite you along, as a way to respect your boundaries.
You aren’t wrong for setting boundaries and she isn’t wrong for wanting to hang out with him, assuming she has no intentions of being intimate with him.
Communication is the most important part of all this, though. And communication has to go both ways.
The fact that she isn’t telling her non-romantic male friend about you is very concerning to me, honestly. I understand wanting privacy but honestly, there is a bit of a concerning trend with her it seems. Talking to her is the absolute best thing to do though, so it sounds like you’re on the right track.
Wishing you the best with all this.