The terrain is also a factor, if the deer is on flat ground then it is much different than on bumpy ground or near rocks. I use the Fenris armour and claws to run the deer down and whack em. Even when chased they periodically slow down and turn towards you, especially when near rocks and trees. Also all those little bushes and stuff get in the way when you shoot.
Anyway, it could be what you are seeing is a reaction to the terrain and it is coincidental to you shooting the arrow. Dear also tend to path back to spawn points when frightened, most animals do. I once dragged a boar a very long way, and when his pen got trashed before being tamed, the thing ran off at warp speed in the direction I gathered it from.