The easiest thing to do is to look at the e-ticket receipt. It will show charges, if any, for the first and second bag.
The real question is whether they are merely seated in Y on a C ticket. If this is the case, the baggage allowance ought to be the C allowance. If it's ticketed in Y, the allowance would be 0.
Why not report back once you've had a look at those receipts. Then maybe you'll have your answer and you can certainly get advice here if it's incorrect.