There are many discussions about this DLC on the forums here and many interpretations.
If you look at the Divide Map though, Ulysses temple is in the west and you have to walk towards it. It's like a large circle, first you head east, then you go through the Cave of the Abaddon, and when you come out, you should be heading west again.
I just like to think that my courier traveled to and from the Divide, but never paid it much attention. It was just a place for her. She made her deliveries and that was it. That's why she doesn't remember much about the place. East , west, what does it matter to a courier, who's used to walking the Mojave in any direction.