No, you're not being unreasonable. This is a both of you thing. Either you're both on board, or it's a no go. That your wife says you're being controlling and not trusting her is all the more reason to pull the plug on this. I'm seeing red warning flags all over this. This isn't going to get better by her playing alone with this guy. That will only make it worse. I'm sorry for her, but either she's committed to you or not. This shouldn't even be a question.
The only caveat I'll put in this is that we're hearing your side, and not hers. But really, I don't think I need more to go on here. You're not comfortable with this. That should end it with this guy period.
My wife has had two long term boyfriends in the past that she played solo with many times. That worked better for us, having kids at home. Scheduling was difficult, and if she were to keep these men happy and interested, solo play was going to have to be a part of it. We agreed to that before going down that path. Had I expressed discomfort with that, I have no question she would have stopped it immediately. That's part of what made me comfortable about it; knowing that we were a team, even if she were playing solo.
Your wife may really be clicking with this guy, and that would likely make the sex all the better for her. So, I'm sure it's disappointing that this wouldn't move forward. But, is she willing to sacrifice you in the name of finding a fun sex partner that she clicks with? Really?
End the relationship with this guy now.