I had similar problems with my siblings as a child. My parents didn't know I had ASD at the time, and it was a real problem.
Basically, they handled me the same way as they would any other child: I was punished for hitting, and more so when I was the perceived instigator. In retrospect, that wasn't always fair, but in most cases it was appropriate and in most cases it worked.
Why wasn't it always fair? Had my parents known more about my condition, then they'd have known I had a unique set of "triggers" for violence. My sisters would constantly touch my head to tease me, which I hated. I generally never wanted them to touch me. They weren't often violent with the touching (though sometimes they were), and no matter how often my parents disciplined me, I was never going to tolerate unwanted physical contact from my siblings. Also, there were situations with loud screaming and noises - one sister in particular would talk too loudly and the other screamed in high pitches. This caused me pain, and they may as well have been hitting me first. My parents didn't know this either.
Conversely, when I had been at fault, though, I accepted the punishment as just and learned from it. When you punish a child, however, for something that he did not instigate or does not understand, then the child will learn nothing from the punishment.
The solution? Make sure your child knows the reason for the punishment, and make sure you are not punishing him for things that are not his fault or over-punishing him and under-punishing others because you mistakenly believe he is the instigator. That can be challenging when you don't observe what happened.
Also, as I presume you are NT, you may need to really educate yourself about what it is like to be your son before you will be able to appreciate how things affect him differently. When I was a kid, I'd have preferred my sisters hit me rather than talk loudly or scream, which they frequently did. My early childhood was torture when my parents weren't around because my sisters took advantage of my parents' ignorance to paint me in a bad light. As the years past, my parents eventually caught on to the truth.
I don't know if any of this applies, but I hope it helps.