Jim,
My (81" ) Cub requires using right rudder for a right turn, but it also requires adding a little left aileron in that same right turn. And yes, trying a turn without opposite aileron results in a turn that quickly tightens into a spin. (A lot "roll coupling" on the rudder.) All of this is true whether right or left by the way.

It's the only Cub I've flown, so can't comment on others, but I let a friend at the field fly it and he said, "flys like a Cub".) He's had a few, included 1/4 and 1/3 scale, so....
Dennis-