First of all, thanks you so much for your detailed and kindness answer!
I will try to explain as accurate as possible now.
Everything you listed is right, rcs, good design, SAS on..
What I meant with "start spinning" is that I never could get roughly lined up. I mean, the two ships had their docking ports looking other sides like this pic from your guide.
After reading your very useful guide (thanks, for real) I realized that, as I was in the tutorial, I could't move the other scenario-to-dock-in ship!! So it was nearly impossible align my vessel with the static (and uncontrollable) one. Thinking it now, it's easier to align them if I control one, then the other and I align them, not only one as I tried in the tutorial.