Another quick Irish picking related question

When you are picking an Irish tune, you're supposed to only move your wrist while holding your arm still, right?
Well, while I certainly pick using my wrist (as opposed to picking by moving my thumb or arm), my arm still kind of sways along with the rythm of my wrist.
Do I need to try to fix that? Because so far, it seems pretty impossible to do so, especially while picking fast paced reels.

Thank you very much in advance.