His female roommate is giving me anxiety

fearfulanxious , it is very good that you stopped to try to understand your feelings here instead of just acting out with your triggered state -- because you very clearly are triggered! The fact you are aware of that though and stopping to question it means you've certainly done some early attachment work so far, so keep that up.

I have found that when an AP or FA is triggered anxious, it is because something has brought up their fear of abandonment. This might be real or it might be projection from an earlier time in life that seems like it is because of the current situation but actually has nothing to do with the other person. It's good you're asking that question (is it you or is it a warning sign that you should run away from him). Sitting with issues, connecting with yourself to see why you feel a certain way about something, and if it's really a you problem (ie projection from the fearful avoidant attachment issues), a him problem (ie he's not communicating well, is being immature, is acting out for reasons that have nothing to do with YOU but are about his issues), or a problem between the two of you together (incompatibility in the relationship). It sounds like, in this case, you do not know him well enough yet to know if it's a "him" problem, but you know that jealousy and fear of abandonment is a you problem. You would be triggered this way with anyone in a similar situation, and it is not because he did something (yet) that he knew was disrespectful of you or your boundaries.

It is very scary in this situation for someone with an insecure attachment style to share your needs and feel vulnerable. That is why you do not know how to bring this up "maturely." When someone is triggered anxious, they do not know how to emotionally self-regulate and want someone else to make it better. They want connection to soothe their anxiety. But they are afraid that sharing their thoughts and asking for this will repulse or scare the other person away, most likely because this was all learned from similar experiences earlier in life from someone who did not make you feel safe but who you also had to emotionally regulate (ie situations where instead of a parent parenting their child, the child has to figure out how to soothe and parent the adult... then when the child grows up, they don't know how to soothe themselves but feel they must be hypervigilent to the feelings of others).

The solution is to practice sharing your thoughts, to communicate directly, and be vulnerable, even if it is scary. I had to force myself to do this over a year or two, even though I'd be scared to say what I wanted in case the other person thought it was too needy and left, but practice doing this with the people you care about is necessary! If it is someone you can trust, you will see that a small conflict will not cause the connection to break. If it is a person who will be good in a relationship, they will listen to what you have to say and work with you to see if the two of you can solve the problem. If the person has their own attachment issues and gets triggered because you are bringing up an issue important to you and they either get angry or shut down, then that is going to be a difficult person to have a healthy romantic relationship with while you are also, on your own, working out your attachment issues and trying to get more secure.

What I see is happening from what you've posted is you are very scared to admit how you feel in case he responds in a way that hurts you, so your FA pattern is telling you to run away instead of talking to him. However, because you have not communicated your needs or how you feel with him and he doesn't know them, he is not working with you to fix the problem since he cannot read your mind... but since you feel fear, the longer it is not feeling addressed the "worse" you feel that he hasn't fixed it already. Then you feel unsafe, like he doesn't respect your boundaries or defend you, and so want to push him away. If you try to protect yourself by taking distance and not telling him the problem, you will sabotage the relationship. Relationships need good communication on both sides, and you cannot control his side or mindread his side or expect him to be able to read your mind, but you can practice being a good communicator on your end and talk through how you feel. This will start to build trust, as you will see if he respects your boundaries and your needs or not.

That is why I am saying this is partially a communication problem and that the only way to feel better in a constructive way is talk to him.

I think how I phrased it before is good. You have never dated someone with a female roommate, and you feel confused because it honestly makes you a little uncomfortable. So you will feel better if you two can talk about it a little, how he knows her originally, and if there's anything you should know that's ever happened between them before. Again, if he answers your questions and says everything is okay, then you respond thank you for answering my questions. I do not want this to cause a problem between us and respect that you are just roommates. The only thing I'm still uncomfortable about is she does make some jokes at my expense, and I would feel better about it if she wouldn't do that. It is a new situation I am still getting used to, and that will be easier if the jokes stop.

If he thinks you are making too big a deal or tells you to suck it up and the jokes are funny or whatever... then you are learning information about whether or not you should trust him. He is showing you if you can trust him by whether or not he'll be respectful and take you seriously. If he doesn't, then it shows he may not be a compatible match because you deserve respect. That doesn't mean he's bad or you're bad or even that the roommate is bad, it just is what it is.

On your own, as you deal with your FA style, you fear abandonment because you don't know how to self-regulate your emotions and don't have all the tools to not abandon yourself. So to counteract fear of abandonment on your own, separate from a relationship, is about building your self-esteem and self-acceptance. So, working on it in a relationship involves practicing good communication. On your own, you also need to work on this self-esteem -- no partner is responsible for giving that you, only you are responsible for it yourself. Partners should act respectfully and with good boundaries and communication, but if he hasn't given you a reason to distrust him yet, and you like him, don't write him off yet.

Have you been working with a therapist on healing your attachment issues up to this point?