Local coordinates are inconsistent for non-player entities

The bug

Local coordinates (^ ^ ^) are supposed to point relative to the direction the entity is facing. This works for players, but is not consistent for other mobs.

How to reproduce

1. Download the attached world
2. Walk around the enclosed mobs

Expected behavior
The particles indicating the direction of ^ ^ ^3 for each mob should match the direction that mob is facing, like this:

Observed behavior

As the mobs turn around, the particles remain in place, indicating that the direction of the local coordinates is wrong.