Evidently, the idea for the Cessna 208 existed before FedEx got involved. Cessna started with a widened and stretched 206 fuselage. It was designed to replace the aging De Havilland Canada Otters, Beavers and Beech 18 aircraft in use with bush operators.
Marketing surveys from the late seventies concluded that a modern, large capacity, rugged single engine aircraft for sale could compete successfully...
They completed the first flying prototype and were expecting orders mainly from the target market of bush operators. However, the CEO of FedEx saw it on the cover of Flying Magazine and sensed opportunity. (Whether this is true or not, FedEx was looking for a small aircraft to replace trucks on some routes, and the Caravan came along at just that time.) Cessna made some changes such as adding a cargo pod to create the Cargomaster. The big orders from FedEx helped to drive the popularity of the Caravan.
So FedEx was not the reason for designing the Caravan in the first place, but it was a big part of the success of the design and did influence some aspects of it.