Are you referring to the speed trim system....that levels the fuselage in forward flight by means of an air speed sensor and electric powered actuators that tilt both the forward and aft heads as forward airspeed varies?
Forward and Aft cyclic movement varies pitch angles for each head...adding pitch in one and decreasing pitch in the other.
Thrust (collective lever for kids who fly skids)....increases or decreases pitch in both heads.
The only unusual flight characteristics I recall from flying the Chinnok stem from it being a tandem rotor helicopter.
When making takeoffs with no power margin (yes....one can overload a Chinook)...keeping the aft rotor in clean air by either side slipping or adding right pedal as ETL is reached will allow one to carry heavier loads.
Another interesting experience is "falling through" on landing. Arrive a bit too fast and heavy with a strong deceleration can wind up with you having to apply forward cyclic to level the aircraft which only adds to the sink rate caused by a lack of power. Add in a tail wind component and it gets un-boring quickly. Again....keeping the aft head in clean air prevents a variation in lift the two heads are making.
The one very nice thing about the Chinook is the 144 inch allowable CG range. CG problems are fairly hard to acheive due to the tandem rotor configuration.