As far as the what its with him being armed.. too many what ifs. I don't personally jog with my firearm. But I can say I do chase after guys on a fairly regular basis. So what would happen if I was chasing someone and cane around a corner and you were there with a gun? Depends on both parties. You verbally made him aware that you were not a threat and he did the same. If I came around a corner and saw a gun and you immediately said "s**** sorry you scared me". Then no harm no foul.
I'm sure others will be on to tell you that it was dumb to that but I agree with you and what you did. Great example of that extra step needed to deescalate a situation.
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