I've referenced my James Avery crosslet ring before. Originally a gift from my late sister that I literally wore out, and then a new one as a re-gift from my wife and daughters.
For the first roughly twenty years I wore this ring, including both pre and post conversion, I wore it with the cross facing me. Oriented this way it served as a reminder, and as a comforter, to me. It was aimed at me for my benefit.
However, after I assumed my "evangelical" identity, the next two decades have found the ring rotated so that the cross now faces away from me towards other people. Instead of being a private devotion, it is now an outward proclamation.
The ring's position on my hands reflects my own metamorphosis from inward pietism to outward evangelicalism.
BTW: There is no "correct" orientation for the ring. I only speak of and from my own experience.