I've had great lucky hunting with a 6mm Remington CoreLokt in the past, almost all deer are deader 'n dead by the time I can get to them.
Once and only once have I made a follow up shot on a deer, mostly because I thought I'd only nicked him. He staggered and then proceeded to try to discern where to run to get away. I followed up which knocked him down, but he immediately came up to run again. Sadly, were so close to land we couldn't pursue on to I shot him a third time, thinking some how I was missing, or nicking him. The third shot put him down for the count. In butchering we found all three holes, all three penetrating the main chest cavity, but we never did find any evidence of lungs or a heart anywhere, they were pretty well just gone.
In retrospect on that count, I kick myself. He was pretty well dead on the first shot, he just hadn't realized it yet. The level of shock he was in he couldn't feel anything. Unlike humans, he didn't know that when you get shot you're supposed to die though so he kept trying to run, and I being inexperienced at the time thought that meant I hadn't placed my shot well enough.
So, long story short, I only follow up if they're still trying to get up and run. Any kicking on the ground, etc, is simply the nervous system shutting down and the result of random synapses firing due to shock and not an actual sign of life.
On a side note, with small game, I was taught if you're going to butcher them, but the twitch isn't gone, use the rear legs as a holding point and smartly smack the skull in to a solid object. Less meat damage that way, but brings a more abrupt final nervous system shut down.