As far as I'm concerned, when I play, while Connor is in the middle of the animation of killing someone I keep my left stick pointed to whoever I want to kill next (just make sure they are a reasonable close distance to you).
When the animation is ALMOST done, press square while your left stick is still pointing toward your next target. That's how it works for me at least. I've never really noticed how I've been doing it so far since it seems so normal and casual that I'm used to it. Not sure why you're having so much trouble :P