I think most modern hunters put a premium on a quick and efficient kill (and not wasting anything.) I don't think ancient hunters could always afford that luxury, or that they needed to.
I imagine a lot of times they would sink a couple of dart points in the lung area, and then just hang back and wait. If the animals were near water or a marsh, the animal probably just stayed there and died hours or days later. Modern elephants will stick around an injured animal, so if mammoths/mastodons/gomphothere were similar to them in that social behavior, that might explain a couple of the multiple animal kill sites. (Get one, see of others stay, dart them, and wait for them to die.)
Big bison jumps out west probably operated similarly, maim a bunch of animals and then butcher them. If the animal is still alive, you've got a bit more time to butcher other animals.