pprune fan #1 and helmetfire,
You can see the natural behavior of the rotor even on a stabilized helo if you wantch the sas actuator behavior on the little window most systems have. Select the axis you want to examine, and note what the sas has to do to keep things normal. After all, those little sas actuators are just small pilot input devices for the autopilot.
In pprune fan's sideward flight experiment (which helmetfire has diagnosed correctly) just see what direction the inner loop must input to keep the bank.
Most rotors try to "back flap"when a speed or wind increase is imposed on them. That is due to the fact that the blade that sweeps into the increasing wind gets more lift (from its increased speed) so it flaps upward. The full effect is felt approximately 90 degrees later, so the rotor disk tends to flap away from the speed increase. That is one of the contributers to the dihedral I mentioned for the last two posts.