Oil that up and it’ll look red again
to me that looks like pigmentation from the wood, although definitely more prominent than mine but still the same hue nonetheless. That faded look on the wood after you rubbed it is what wood looks like stripped of the waxy / oily finish.
I get brown stains when I wipe the mineral oil off my Firewood when I clean it too. And my Walnut Vapman. It just comes down to the wood.
Something else that can happen I think, if an oil rich finish is applied too thick without polishing it off, it can also cause the pigments to leech the longer it sits. But that’s probably reaching on my part.
I’d wax it up if I were you, and go through a couple cycles, it shouldn’t be coming off on your hands.