Dear Suta,
I think this CMFB can not be described as a genearl CMFB, complete operation of this circuit I guess should not be seperated from the main amplifier,, Otherwise according to your last statement, you are treating the common mode input as it is the same if it is the output common mode voltage in which the circuit work as follow
if input common mode voltage (vin1+vin2)/2 > VCMin, currents in M1 and M2 increase in comparing to the currents in M3 and M4, since the current in M13 and M14 are fixed (current source transistors), this lead to decrearse the currents in M5 and M6 thus it tries to rise the output voltage. Reverse mechanisim will happen if (vin1+vin2)/2 < VCMin.