Would you get upset over your FWB flirting with your friend?

For context, me (21F) and him (21M) are in the same university club, and agreed to have a secret, casual thing (no sex, like making out and more). I understand that it’s non committal etc, but recently my friend in the same club told me that he tried to hit on her. She knows about us, but he does not know that she knows, and told her that there was nothing going on between me and him. I get that part, since we agreed to be secret, but would it be haughty of me to tell him I can’t handle him flirting with ppl in the same club (especially our mutual friends)? It’s less out of jealousy/having feelings or anything since I would get him flirting with other girls in general, but him flirting with my friends or just ppl we know and hang out with mutually feels a bit gross and a recipe for a mess. Obviously it’s his choice since we’re not together, but I’m just wondering if others would feel iffy about their “fwb” flirting with their friends, or if I’m just not cut out for this.