There's no validity in self diagnosing tbh. What appears as anxiety in someone may actually be ADHD, and what looks lie ADHD in another person may actually be signs of autism. Neither you OR him can say what he has, because you simply don't have the education or qualifications to do so. So it doesn't really matter if he calls it autism or ADHD at this point, since it wouldn;t be a real diagnosis.
What you COULD do is bring up kindly that the symptoms he has listed to you sound like they might be ADHD, too, and ask why he thinks it is autism. That way you are not necessarily saying he is wrong or disagreeing, but just offering another possibility. It is worded as support rather than a contradiction.
Until he can get a real diagnosis, the best you can do is look up the matching symptoms AS WELL AS coping skills and practices for any that he feels hinder him. Someone with ADHD OR autism OR anxiety may benefit from things like breathing exercises, overstimulation avoidance practices, and acceptable self-stimulation aspects like little fidget toys that allow your hands something to focus on and calm the mind. Keep in mind that the stats show there is a big correlation between ADHD and autism- severe or even moderate ADHD can overlap with autism and Aspergers in a way that the symptoms and impacts they have may be difficult to tell apart, based on how that person is affected by them and how severe theirs is.
