Timing is achieved by balancing housing pressure with transfer pump pressure and the "leaky" piston is in between. Housing pressure goes to zero so the advance piston gets 100% of the transfer pump pressure and flow to slam it full advance. Without cold advance the housing pressure is higher and the piston leaks - well there isn't as much force available and the piston due to the leak isn't as advanced as it should be.
Their explanation of the light load advance is confusing and in error. From the site:
A light load advance mechanism provides advance when the engine is operating at low speed or under light load, when the transfer pressure is too low to move the advance piston.
The light load advance is actuated by an external face cam and rocker lever assembly when the throttle shaft rotates (on the 6.2L and 6.5L engines, this mechanism is on the passenger side of the pump). The lower end of the rocker lever pushes on the end of the servo advance plunger.
As the throttle shaft rotates, the face cam pushes on the rocker lever using a “see-saw” action, which depresses the servo plunger and
advances (No opening the throttle and ramping the lever on the cam retards the timing. The correct word here is retard... and in more ways than one.) the timing through the power plunger’s linkage to the cam ring. At a predetermined angle, the face cam flattens out, so that additional throttle movement does not affect the servo.
http://www.oliverdiesel.com/tech/howdb2pumpworks.htm
The HPCA solenoid is located under the fuel return outlet, under the pump housing cover. It is activated by the coolant temperature switch, which is mounted on the rear of the passenger side cylinder head. When coolant temperature is low the temperature switch is closed, energizing the
HPCA solenoid (rear pump terminal connected with a green wire), which lifts the check ball off its seat in the return outlet. This reduces housing pressure to near zero, so that the transfer pump pressure behind the power advance piston can easily advance the cam ring.