Theoretically, you shouldn't have to tilt your head if you are shooting instinctively. Your brain should be able to figure out the variables, without needing to define them all in words, and eventually you should be able to hit your target.
However, if your eye is not over the arrow, it does add another variable for your brain to figure out: that the arrow is coming toward the target from the side, rather than from directly under your eye. The point of your arrow, blurred in your peripheral vision, will necessarily have to be to the side of the target rather than directly under it, and the amount of offset of the point of the arrow to the target will change with the distance to the target.
Because of this, most, though not all, instinctive shooters prefer to get their dominant eye over the arrow, and the usual way to do this is by tilting the head.