General description: 

The direction arrows are facing does not, in general, align with their visual appearance and their "Motion" nbt tag. The x- and the y-direction components point from tip to tail, while the z-direction component points from the tail to the tip. This affects tp ^ ^ ^1 execution, resulting in an illogical arrow movement, as well as other dependent actions.

What I expected to happen was:

Either the arrow entity faces the direction it is/was moving (preferably) or the complete opposite direction.

What actually happened was:

Components x and y point in the direction the arrow came from, while the z component points in the direction of the movement.

Steps to reproduce:

1. Take a bow and arrows
2. Shoot in any direction
3. Observe the direction the arrow is facing

Additional information:

Seems to be present in versions all the way from 1.8 even 14w29a (F3 + B introduced several snapshots prior, could not load them) up to the latest snapshot 20w18a.

Everything said applies to tipped arrows and spectral arrows.