Well, I would assume that snapping to tiles does either one of two things:
1. Once dragging begins, all sprites snap to the nearest tile.
2. Once dragging begins, the sprite under the mouse pointer snaps to the nearest tile, and all other sprites snap the same distance.
From there on, all movements are relative to the position of the sprite being dragged by the cursor. Personally, I dislike systems that do #2 and always thought they should do #1. After all, you do have "Snap to tiles" turned on
Also, even if you don't want to fix it for multiple sprites, when only 1 sprite is being dragged this isn't a problem, and that's the majority of sprite movement, at least for me, and the reason I move sprites is because the map has changed, and I still want the sprite to be aligned to tiles.