Wow, I'd never heard autism could cause reactions to vaccines. I know little about autism (probably nobody knows much), but I always thought it had to do with one's mind (from what I studied, the guessing pointed to a disability in the linguistic spectrum, not understanding that we are all individuals with individual thoughts and thus having difficulties when communicating). Unless, of course, a patient has other medical issues as well, which happens more often than we would like.
No idea why your son reacted to the vaccine, but maybe he just did just because he is sensitive to vaccines (aside from having autism).
My sister also has medical issues (both mental and physical) but if she happened to be allergic to pollen, I wouldn't think it was because of her main illness. Just that, well, she was allergic to pollen too.
No clue whether he should take another shot, maybe you should wait for a while, but I'm no doctor.
ETA: Also, could it be possible that children with autism are more prone to vaccine sensitivity because they don't understand what is going on, can't communicate their fears, and this causes them stress and thus unwanted reactions? Just taking a guess here and trying to understand where the relationship autism-vaccine comes from...