@scootch I believe your question is more asking whether the teens are allowed to do the excursion without you, rather than related to going tandem for their actual parasailing ride. I haven't cruised with a teen (yet) but I did find on
DCL's website about the parasailing on CC: "
Children aged 13 to 17 participating unaccompanied must be escorted to Marge's Barges by a parent or legal guardian." It's in the Know Before You Go section. That sounds like you should not have to pay for yourself, only the teens, and escort them to Marges Barges for the excursion. It specifically states no ride-alongs. I didn't check any other parasailing excursions at other ports; they may have different rules.
Note there is also a Wild Side Teen Adventure offered, though it does not include parasailing. I'm not sure if a 13-yr-old would be allowed, but the 16-yr-old might be interested.
Enjoy your cruise!