It would help to know the history between your gf and this man. How long have they known each other?
Here's the thing: they have rapport and connection that pre-dates yours. Even if it was never sexual or romantic (if they're both attractive, that's doubtful), you need to understand that demanding she cease contact with a close friend is not only not going to happen, but it will make you look jealous, controlling, and fearful -- insecure. And you will attract what you fear. Behaving in an insecure manner will quickly drive her into the arms of another man, whether this guy or another guy she has in the wings.
On the other hand, if you expect a relationship to work, you need to communicate. Most of the "be alpha, hold frame, act aloof" advice is for the attraction/courtship phase. You're now past that, in the relationship phase. Of course, you still need to behave like a strong, masculine man -- but now, you have a right to make yourself heard. If something bugs you, you need to clear the air.
Tricky part is, understandably, that clearing the air on this will make you look a little insecure and vulnerable. There is a fairly likely chance that there is honest-to-God nothing going on with her and him, and you have nothing to worry about.
But if you expect this relationship to last and be fulfilling, you have to communicate your feelings and boundaries to her. If you want a relationship to last, you can't be scared of being a little vulnerable. Be emotionally brave. Otherwise, this is just a fling or a "plate" as per the forum parlance and you should expect it to be temporary.
Don't make this an ongoing thing. But bring it up directly. "Hey, I get that he's your friend and nothing's going on, but I feel disrespected that a week after you ask me to be exclusive, you're Netflix and chilling with a guy alone in your apartment, and acting like I'm supposed to be totally cool with it. I'm not going to stop you or forbid you from seeing your friend, it's not reasonable of me to do that. But you should know how I feel about this. That's all."
Don't give her ultimatums. Don't make her promise you anything. And don't ever bring it up again. State it once, directly, and clearly. Clear the air, and observe her reaction and subsequent behavior. That will tell you whether this woman is a worthy candidate for you, or just a "plate."
Pretending that you're aloof and unconcerned while you're bottling up resentment is not going to make this a healthy relationship, if that's what you want. Being afraid that you'll come off as insecure and jealous is also fear-based mindset and it's unattractive.
If she's going to hook up with this guy, nothing you do or say will stop her. If she's a cheater, she's going to cheat on you eventually, regardless.
If she cares about you and wants this relationship to work, she's going to listen to you and validate you. If she's totally turned off by your insecurity and weakness, well, something at some point was going to turn her off so might as well enjoy the ride while it lasts.
Generally speaking, dating attractive, extroverted women with a lot of guy friends is seen, justifiably, as a red flag. But going around continually distrusting a partner is not a relationship worth having. So you have to trust -- but verify. You are now exclusive, and you now have a right to information about her and who she's hanging out with. If she acts like you have no right to her personal life, she's not your girlfriend. Period.
Make your feelings clear, observe her carefully thereafter, and have a foot out the door. This is the probationary period. If you sense deception, or that she starts distancing herself, be ready, willing, and able to walk away at a moment's notice. Don't tell her that you are, just be ready to do it, and do it when this relationship no longer makes you happy.
