You had two lines going at the same time. The line of sight from your eye through the sight pin to the target, and the line of arrow launch from your anchor through the rest to the target. Your line of sight was shifted left in relation to your line of launch. By moving your rest left without moving the sights, you were moving the lines closer and closer together until they merged.

Since your groups tightened up and visible fishtailing went away, I' d say your centershot was off to begin with, maybe causing your arrows to bounce out of the rest and head off to the left instead of along the original line of launch (wierd things happen, sometimes), and it may still be off. But you' re probably a lot closer than you were.

That' s all assuming your arrows are spined properly. If not, that throws a whole nuther monkeywrench into the works.