CL12..:
L = (1/2) d v2 s CL
d, s, are the same on both sides of the disc (adv and retreat).
The formula is balanced due to flapping to equality in fwd flight (or in the hover with a wind).
When you lower the lever, the CL changes on both sides by the SAME amount because it is the collective (thanks for reminding me!).
Part of the coeff of lift is the A of A. It is this which is reduced (collectively) on the adv and ret side.
The instantaneous effect of "destabilising" the lift formula is a reduction of CL by the same amount, but when this is factored into the above formula, you will notice that the side with the greater "V" inherits the greatest reduction in overall lift (L).
The blade then starts to dip down on the advancing side due to the relative reduction in lift on the adv side. Phase lag causes this effect to be experienced approx 90 degrees later at the front of the rotor plane. The rotor dips down and aft cyclic is required to return the a/c to stability.
If my memory serves me right