Lu,
In an attempt at clarification I muddied the waters - my simple 2 bladed model had double correction for phase lag, both swash plate tilt to the right to produce blade low at the front and a 90 degree advance angle on the pitch operating arms. One or other of these corrections would have been alright and the aim was to agree that the blade reaches it's high or low position 90 degrees after the maximum or minimum cyclic pitch position.
Most real helicopters use a combination of jack positioning and advance angle of the POAs to achieve the obviously desireable state where forward cyclic makes the blades flap down at the front and up at the back, thereby angling the Total Reaction forwards and accelerating the helicopter.
If the FAA thinks that differential airspeeds on the advancing and retreating blades makes the aircraft roll left then good luck to anyone flying a helicopter certified by them. The true result as we all know is flapback (blowback).
The roll towards the advancing blade (to the right on a counter-clockwise rotor)is a result of disc tilt causing a reduction in the inflow angle at the front of the disc. The increase in AoA gives more lift and as the effect starts at the 3 o'clock position, has it's maximum at 12 o'clock and reduces by the 9 o'clock the disc flaps to the right (90 degree phase lag again). We call it Inflow Roll and you call it Transverse Flow.