Assuming this is a pencil urchin, they are one of the few species of urchin that have stuff grow on their spines. Unlike other urchins, the spines of pencil urchins do not have living tissue covering them. Hence, many things may settle and grow on them. It is possible that there was coralline algae, for example, that has bleached to white. Without a picture it is difficult to tell. If the white patches are not on the body of the animal, then it is probably not a disease, but it is definitely not related to spawning. A picture would help.
FYI if it is in a reef tank: This is considered to be one of the few "non reef safe" urchins, and will consume just about anything in its path, such as algae or polyps.