I wouldn't be that worried if the surface color occasionally is a bit dark. If it starts to smell bad then there probably is something wrong. Or if there is a soft, partially rotten spot.

Otherwise, the general idea is that a wooden cup is protected by salt and oils, which typically are soaked into the timber before selling a cup to the customer. Therefore it is wise not to use any chemical to wash up the cup - it is enough just to rinse with water (Ordinary dishwashing liquid will dissolve the protective oil, leaving the timber more vulnerable). Another tip is to rinse the cup with black coffee - the liquid will dry, but tiny amounts of oils and acids of will seep into the timber, helping to maintain it.