Oskurito started down the right path... but he went somewhere else with it.
@
S
SeeRaY
You pivot in your shine because you aren't holding on the exact down direction when you press the shine. You are actually holding another direction (the opposite one of the direction you're facing) along with down, which makes you pivot. I've come to realise that this is a problem for me as well. By observing this, I have learned that I don't really need to be holding on the exact down to do my shines. Its actually better when I hold the appropriate downwardly creased position when I shine for the outcome that I want.
What I believe you then need to do is, practice holding the downwardly direction that you are facing (unless you intend to pivot in your shine) to ensure that you do not pivot in your shine. You'll then notice that your character no longer pivots.
Something else that came to may attention, based on this realisation, is how easy it is to do, run -> pivot shine -> WD -> edgehog! Those are really just fundamental moves with the inclusion of that explanation I just gave on holding the opposite crease with the shine. You also find that your character doesn't really lag too much in pivoting either when you hold the direction from the get-go.