The disc rolls to the side, rather than pitching backwards as one might naively expect, because of phase lag.
For systems that are hinged at some distance from the axis of rotation, such as an articulated rotorhead, the phase lag is less than 90 degrees.
In forward flight the pilot will experience either a right or left roll, depending upon whether the rotor of the helicopter rotates counter-clockwise or clockwise respectively.
If a helicopter experiences a crosswind, the transverse flow effect will result in a pitching up or down instead of a roll.
At higher airspeeds, more and more of the rotor disc will be in clean air and the lift differential will decrease, however transverse flow effect will be experienced to some extent across the whole flight envelope.