I may not be able to offer the best advice, since I'm not really sure what it means to "process emotions." I feel what I feel, and it's not until the episode has blown over that I can "process" what happened. For me, it's about understanding what kinds of things set me off and trying to keep those triggers to a minimum. It's about reminding myself that other people often do things without thinking--and certainly without thinking about how they will affect me. Cognitive distortions have a lot to do with the intensity of what I feel, so try to figure out which cognitive distortions (example: over-generalizing, personalizing) play a part in your son's emotional reactions.
He's thirteen, though, so it's a tough time for developing emotional maturity.