I can confirm the exact same thing happening. I had to reload an old save. It works ONLY when you first arrive in the room. Leaving in any manner causes the glitch to occur. I have tried fast traveling out, camping and even leaving the sub area all cause this to happen.
I have also found that completing the puzzle causes it too. If you save immediately after and reload the save, the puzzle will be glitched.
When the puzzle is glitched, the tiles seems to reset every time you turn them, and the symbols are un determinable. it says moon but turning will change it to a half moon, etc..
Spoiler ahead:
Later on after saving Halson, you will need to go to moonrise towers. This is one of the paths you may take, I have not tried taking the other path yet so i do not know if this is progression breaking or not.
