I summoned Baykok on the surface at y=68, I hit him causing him to teleport, and his healthbar vanished. This happened the next two times. I later found him underground in a cave at y=34, where there was no way for him to have walked down there. He just teleported there.

You should probably make sure the teleport radius is y-capped.

Upon retrospection, the issue could have been the Repellant enchantment which was present on my armor. Further testing is required.