If the pull pull cables are attached to the servo arm that is directly attached to the servo any cable tension is going to pull on the servos output shaft. Thats probably whats causing your buzzing.
I have seen installations where the servo arm has a short pushrod on it that connects to another arm. That arm is where the pull pull cables attach and that arm takes all the pulling load. Not the servo.
Heres a pic to help visualize this,