I would suspect it's the oil, it's only on the tips so it's got to be something they are being exposed to. If it was all over then it would be a top coat issue. This is the typical pattern seen with things like new jeans, food colours (specifically curry/tumeric/etc.) newly dyed hair, etc.
Have you tried swiping over them with acetone to see if it removes any of the colour. You might need to lightly buff, too, but I suspect whatever has dyed them as soaked into the natural nail underneath too so it will be hard to remove.