Darned if I would deploy that chute for spin recovery.
Apparently the Cirrus SR20 is all but unrecoverable in a spin - it's possible, but you have to be very, very, very good and waiting for the spin to happen.
Since the plane has the airframe parachute system, the FAA let them use it for certification.
Me, I'd follow Cirrus' instructions and pull the BIG RED HANDLE.