And if the person you are working for doesn't have a preference?

Since 13 is the number that seems to be mentioned quite a bit, think about it. Yes, someone can speak in such a manner that thirteen and thirty could be confusing, but I've never had this experience. However, "one" and "three" will always be "one" and "three" no matter what.
Another thing that hasn't been mentioned is the speed of the signal. I can indicate 13 before I get done saying it so the scorekeeper will see the whole thing before assuming my "thirteen" is "thirty." Obviously I'm a whole number type of person because I don't really see why I'm going to report a basketball foul differently from every other time I would use the number 13 or any other double-digit number.

JMHO using my version of common sense.