'Whenever the series actuator nears saturation, the parallel trim actuator with full authority moves the stick at a slow rate so as to displace the anchoring point of the cyclic stick and maintain the series actuator around its mid point, thus restoring full authority '
Yes, but that's when 'hands off', and the AP is trying to maintain the attitude. The series actuators do most of the work most of the time, but if the displacement is too great for them to cope with, the parallel actuator moves (and the therefore the stick as well). The series actuator will be moved (by the computer) to its null position. If the pilot wishes to change the attitude, then he presses the trim button, moves the stick then releases it - this sets the new datum for the AP to work to. On most aircraft there is also a beeper trim to make small changes of attitude.