I understand your concern and I'm really glad you asked this question.
It was a behaviour that seemed weird to me too when I first saw my turtles do it. It's nothing serious so you shouldn't worry about it.
The best way to explain it is to think of it like they are stretching after a long relaxing basking session. Maybe it's because they don't move for a long period of time and maybe their legs go numb so they twitch to get the blood flowing again. I did my best at trying to explain it, I hope it helps.
@Sir Max - I wouldn't consider it weird even if he was watching his turtle all the time. It's normal if it's your first time owning a turtle. He obviously wants to observe his behaviour and know what's normal and what's not; this way you'll know that when you see your turtle acting weird he/she might be having a problem.
Check out my blog at: http://turtleaffairs.wordpress.com/
~Charlie - 4 inch male RES
~Charlotte - 6 inch female RES