Hmmm. I haven't played ICO in forever and I definitely didn't recall a waterwheel puzzle (not that I can claim to recall every puzzle) so I looked it up and in the original release, it was only in the PAL version. Who knew? Apparently they've decided it to be a challenge worthy of inclusion in the HD collection.
I wouldn't say that there's a "correct" way. You're doing it how it has to be done. It seemswould seem that key things to bekeep in mind are do not run or jump at an angle and everything else it seems is a matter of skill/timing/luck and maybe "twitching the control stick so that he's facing it" before you jump. One recommendation is to perform the second jump without verifying that you made the first. In this video the poster manages to do it in 3 tries, taking about a minute or so at the trouble part and even wasting some time goofing off - maybe watching it will give you some hints,.