None of this excuses what happened to you, the obvious thing for the baggage employees to do would have been to notice the tags were for the flight you were on then take your bags out and put them on the carousel when your flight arrived, and if they had only left a "few minutes earlier" this wouldn't have interrupted their busy schedule.

That being said, I think a general rule of air travel (this is not specific to Delta by any means) is that if your bag can make an earlier connection, you should look for it in the baggage office upon arrival, even before bags start coming out. I'm not saying you should of have had to do this in your case, but I've saved myself time waiting more than once following this general rule.