Dissymmetry of lift is caused by the fact that rotor blades moving in the same direction as the helicopter are moving faster through the air and thus generate more lift than the blades on the other side of the disk which are moving with the air and thus generating less lift. More lift means a steeper coning angle. From the outside it looks like the cone is leaning away from the side of the rotor disk that is headed in the helicopter's direction.
To maintain coordinated level flight while moving forward in a Kamov contra-rotating coaxial rotor helicopter (like the Ka-50) the pilot has to apply right rudder.
Unfortunately, that's not the end of the story.
......In addition to the right rudder needed due to the differing torque production of the two rotor disks at airspeed, left cyclic is also needed to maintain steady-state coordinated level flight. Hence the left stick and right rudder we keep finding ourselves using. It's natural. And it's right......