RSD is not really something that you "have" as in a medical condition. It is basically a description of an experience that some people have, which is very commonly associated with ADHD, though can also appear in other conditions (like borderline personality disorder, depression, PTSD). There isn't really much research on it and it is mostly an "internet thing" (if that makes sense).
I do think it can be a useful term in that it can be quite a useful shorthand to say to myself "Ah yep, that's rejection sensitivity again!" and it can be useful in the sense that finding out other people have similar intense reactions to things can make you feel less alone. On the other hand I do tend to feel a bit like - is every bad feeling really a "dysphoria"? But I think that might just be me being annoyed by the social media buzzword thing - it's clearly a useful concept. I just wouldn't get too caught up in it being a thing that you can "have" if that makes sense. It's more of a symptom than a separate disorder.
Experts tend to say that it's part of the emotional dysregulation part of ADHD - this is the recognised medical term, if he did want to talk to his doctor about it. Most adults with mature emotional regulation tend to be aware of their emotional state and when they feel that they are ramping up towards anger, distress, excitement etc can rein it in to a socially acceptable level - but with ADHD a lot of people say it's like you don't get the "warning stage" in the middle (I definitely relate to this) so it's almost like a switch flips and you go from perfectly fine to rage or despair etc - a bit like toddlers can do, and this is why any of the normal suggested techniques like take a deep breath, count to 10, go for a walk etc don't work because you don't have a chance to use them before you're in a state where it's basically impossible to access rational thought. Even something like CBT that is supposed to help you correct the distorted thoughts is difficult to implement - because that's thinking/rational again, and it's too late for that. What someone needs to do when they recognise they have got into that despair/rage/etc state is to go and use some kind of non verbal tool, preferably not near other people as you just take it out on them, which is not fair. Whether that's going off to use a punching bag or meditation or rage cleaning or smoking a cigarette or going off to cry or whatever it is. Recognising that you're in an "irrational" state and taking yourself off away from others is helpful (as long as there is no self-injurious behaviour etc). And if it's a very sensitive emotional bruise that gets hit easily, maybe therapy can help.
ADHD medication can help as it can sort of raise the threshold for what triggers intense emotions - at least it does for me. I think another issue in ADHD is that interoception (fancy word for the sensations inside your body - hunger, bladder fullness, tiredness, emotional state etc) is typically poor. I think this is definitely related, because working on this has helped me notice the warning stage, which I didn't think I could before.
Walking on eggshells isn't good. It's stressful for you, it's unhealthy for the relationship if you can't discuss things and it sounds like it's happening a lot, which might be a signal there is something more underlying like burnout or depression maybe? You definitely need to be able to talk about things. After the spiral, does he then recognise that he was spiralling, and is it possible to talk about (anything?) when he is calmer or does it just start everything off all over again? Because that is totally unsustainable and like PP said, miserable to live with. It's fair to be aware of the RSD and for example if you are annoyed, say something like "I am annoyed, but I'll be fine, I just need some time." if he needs that piece of reassurance (but then he needs to let you have the time) - or for example, it might help to have difficult conversations in a less direct way. I sometimes write to DH on whatsapp (even if we're in the same room!) instead of talking out loud because for anything complicated, it's helpful if I can rearrange sentences and paragraphs, delete irrelevant details etc. And it also means that I don't blurt out something unhelpful in response to half a sentence that he hasn't even finished yet. Just slowing down helps rather than quick fire reaction to reaction to reaction, and the process of writing a reply makes me think more about what I'm replying to, rather than my snap emotional response which has probably picked out one word rather than the whole meaning and context of what is being said. Apparently I once told my mum that we used to have conversations sitting back to back so that I didn't have to look at him 
I don't remember ever doing this! But it's possible that it was a similar thing of trying to avoid an intensely emotional reaction getting in the way of me being able to say what I wanted to say/hear what he had to say.