It is possible that your son reports when he has done something wrong because he is a bit less sensitive to the social responses that typically come along with those reports. It is hard to know. On a positive note, it is so important for parents and children to maintain the type of relationship that allows children to report accurately on their experiences. So, I would continue to enourage your son to be truthful.
I just thought of another thing. If he is telling on himself constantly, could he be doing this because he doesn't really know what is right or wrong (or some of the grey areas) and so he tells on everything as a way of checking whether what he has done is good or bad?
Those on the spectrum think in a very literal black and white way. If he does something he knows is naughty he will feel bad about it because he knows it was wrong. He may also feel guilty if he is impulsive because he couldn't control himself or stop himself doing something he knew he shouldn't. He may then obsess about what he has done and he may also literally believe that 'we have to tell the truth'. He won't understand about white lies, or not telling so you don't get into trouble. He will believe that once he has done wrong he needs to tell someone to pass over the responsibility and let go of the guilt. Is he telling about things he has been naughty or impulsive about, or is he telling about other things as well. My son went through a phase that even when his sister had been naught, if she had to go to timeout he wanted to go to time out too because 'something naughty had happened'. It took him a long time to understand that time out was only for the person who did the naughty thing.
The fact that he knows when he has done something he shouldn't is very positive because it shows a high level of self awareness. However you need to keep an eye on this because he will understand he is different and that he has difficulties and that could lead to low self esteem and even depression. Try to get him involved in any clubs or activities that is around his interests or obsessions to keep him occupied and motivated. You may also need to explain to your son that 'everyone does things wrong sometimes'. You may also need to explain to him that some people tell lies etc. If he believes everything that is said to him he maybe gullable and his peers may get him to do things that get him into trouble at school.
He may also have difficulties letting go of feelings. If my son gets upset he says he cannot control the emotions or stop them. So he can be upset, angry for long periods of time. Even when he has recovered, if he remembers what happened, he will again become upset or angry. At school they will need to work on emotions so that he recognises these emotions in himself and in others and he will need to be taught how to cope with emotions. All these things will need to be taught explicitly because they wont come naturally to him.