When someone has been trying to force monogamy for a while and is finally fed up with it, it can be very hard not to go overboard. I know that when I was in that situation, I thought "I sacrificed myself for him for YEARS and made myself miserable. He can be a bit uncomfortable as he gets used to the changes. And if he's not willing to do that, well I'm not willing to go back to being miserable so I'll just end it and be happier for it".
But the fact is that whatever is scaring you and making you jealous or insecure is likely the idea that you might lose her, or the fact that you feel unappreciated. Both of which are probably true right now. By saying "if you can't be fine with it, I'll leave you", she's basically justifying your fears that you are disposable and that you will lose her by going along with it.
Of course, that's not the way she means it, and you wouldn't be losing her because of letting it happen. But knowing that she has told you that, how much harder is it going to be for you to feel confident that it's all going to be fine?
I suggest you have a talk with her. Tell her you want to be supportive, but she also needs to understand that it's hard for you, and that while you understand that if the relationship doesn't work out (and if it turns out polyamory is a need for her and monogamy is a need for you, the relationship can't work out), then it will end, the way she phrased it makes you feel in a very vulnerable position.
While it's probably been a long time for her, and she wants to finally get going, she had a while to think about it and be ready and impatient, while it's new for you, and she's going too fast and it's scary. For the sake of your relationship (and her second one), she needs to be willing to glow slowly, and make sure to give you some of her time and attention.
That doesn't mean going back to not dating that other guy. But that means not ignoring you when she comes home, or just talking about how awesome he is. That means coming home to you and showing you how much she loves and appreciates you, and having romantic dates together, possibly a weekly date night, doing things you enjoy together, and have him not be a subject she can bring up during this specific time that's just yours and hers.
She should be able to talk about him the rest of the time, though, provided she isn't being mean to you about it. If the relationship keeps going, you'll hear about it, that's just normal. It's going to be an important part of her life, and she's going to want to talk about that important part of her life with you.
However, she doesn't have to talk about it all the time. It's reasonable, at the beginning, to expect some time just dedicated to strengthening your relationship so that it can survive the shift due to a new person entering the picture.
If she provides you with the love, attention and care needed to make a relationship feel safe and secure, then whatever she does with him on the time the two of them spend together should not feel threatening to you, because you will know that when she comes back, she will be happy and looking forward to spending time with you, as you are to spend time with her.