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He seemed to really get it and was happy about it.
That kinda says it all, doesn't it? Now only thing left to monitor is how he processes it in the long term, and stay alert for self-esteem issues. And keep sharing information casually, about neurodiversity, the way the brain works, also in other people - let him know he's not alone. You wouldn't believe my happiness when I found out Tim Howard has Tourettes, and my enthousiasm when I got to share that with my kid. (disclaimer: I know, not all non-NT people are superheros, neither should they be, but roll models are important).
Your wife is probably scared and nervous that he would think they're something 'wrong with him'. My kid's dad was the same, but since I'm borderline NT / ASD-ASHD, I understood as well how important it is to get a name for whatever it is that you're struggling with. Otherwise, you just feel like you should belong, but you know darn well that you don't. I think NT people just don't get that part.