I note that the armed citizen felt threatened, but IMHO
I am not sure I would have pulled a gun unless demanding the stop illicited a threat.
While he is holding the alleged thief for the police, remember that if he runs or walks away this is a "No Shoot" situation.
Also, now that YOU have pulled a gun, I believe that it is now inappropriate to follow. Your only action at this point is to make sure the perpetrator does not harm anyone.
Of course we don't know what if any dialog there was between the alleged thief and the citizen. He may have been threatened. In that case the display of a firearm might be appropriate.