You did not overreact. It only takes a second for "playing" to become fighting. I've never been at a dog park with my dogs, 'cause there's none around where I live, but I'd call them in if you see them there again...
I don't think you over reacted at all, I go to the dog park all the time here and if at anytime I think my dog might be in danger I would defiantly do the same thing.
by the way, it is usually ILLIGAL for people to drop off their dogs, next time that happens someone should call the police or animal control.
luckily, the dog park I go to usually...(but not all the time) everyone is good about watching their dogs. (the major problem their is unneutered males that sometimes get to dominant...)