in a climbing turn to the left I need to apply right rudder.
it is a characteristic of the aerodynamics of the fuselage shape and probably peculiar to the W8 Tailwind.
So do I but I think it is due to torque effect, P factor and slipstream effect rather than anything unique to the aircraft type. Also, you need less right rudder in a left turn compared with climbing straight ahead so you actually reduce right rudder pressure as you are entering the turn.