I doubt you have a CPL. If you're not willing to use it to eliminate a threat then why have one, other than to brag to your buddies that you have one?
Based on your comments on this thread, I suspect that if you had been in that restaurant, you would have been scared shitless not knowing what to do even tho you might have been carrying........
I would not have shot him in the back.
At this point, it’s probably a better idea to pull your phone out instead of your gun and dial 911 to report the crime to the police, to start them on their job. Fill them in on what happened, what the crime was, what he was wearing, if he had any weapons, etc.
The argument can be made, unless he had turned around and began slinging bullets in your general direction, that the threat to you was over and that you should not have shot the person. Once that argument is made, it’s not very hard to get to the next argument, which is that you just wanted to kill someone.