SimWes:
The following is based on a foggy and addled memory of the course I did about six years ago, so PLEASE check out for yourself if what I'm about to say is still correct. There was some debate being had at Boeing at the time regarding whether this is a desirable function, or whether it is totally unnecessary. I don't know what the outcome was, sorry.
The rudder is responding to the apparent out of balance condition that the aircraft is in when turning it on the ground. There is no angle of bank, so it interprets the tail being out of line as an uncommanded yaw or the onset of dutch roll, and puts a rudder input in to try to correct it. As the airspeed is very low, (if you're using the tiller it is well below the computational airspeed for the yaw damper system) the yaw damper is limited to a maximum deflection of 3 degrees if memory serves. This will happen irrespective of autopilot or IRU alignment status.
Of course if the yaw damper is switched off, it won't respond, hence why no movement is shown on the SPI under those conditions.
Hope this helps, and would you let me know if my memory is still good?
Rgds
P J