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 seems to be a matter of skill/timing/luck. In this video the poster manages to do it in 3 tries, taking about a minute or so at the trouble part - maybe watching it will give you some hints,