Rancidity (DOS) can turn soap an overall orange color if an ingredient throughout the the soap is going bad or if the soap is exposed to something that causes the soap to deteriorate. Possibilities -- Exposure to strong light. Something in the atmosphere in my friend's bathroom cupboard (I have no idea what!) Oxidized lavender EO. Fats going rancid.
Spots of DOS are more related, IMO, to small bits of contamination, such as trace metals, that trigger rancidity in a limited spot. Possibilities -- Handling soap with dirty hands. Tiny flakes of metal off utensils. Tap water with trace metals. Storing soap on a metallic surface.