Hard to say without the offsets listed. Find out the offsets or have him send a photo demonstrating they fit a Cayman.
For a Cayman S the factory wheels should be
20 x 8.5 ET 55 front
20 x 10 ET 45 rear.
Although the tire sizes listed are indeed for a Cayman. New Sport Cup II tires would be $1890, so that is a decent deal.
Perhaps he is confused. There are several models of wheel that were available on a Cayman S with Carrera in the name - Carrera S wheels, Carrera Classic wheels, Carrera Sport wheels, etc. Doesn't mean they will fit a Carrera, that's just the name of the wheel.