Since Richard answered that 3.5 years ago, and since I know too well how hard it can be to tune a Plus+1 PID loop, I'll take a shot at it.
I think he is saying that his software knows the engine speed somehow, maybe through three digital inputs (one for each of the three speeds settings), or with a pulse pickup, or with J1939. If designing something, note that the digital inputs reflect the speed setpoint, which would lead the actual RPM, while the pulse pickup would most closely match the actual RPM, and the J1939 would lag the actual RPM.
When his software sees a sudden change in engine RPM, it needs to suddenly change the PID output so he forces the 'I' portion of the PID controller output to a new initial value which he has calculated from the engine speed and other parameters. If the engine speed increases, he will need to reduce pump output to get the same oil flow rate so the new 'I' value would be small or even negative for make this happen. And if the engine speed suddenly decreases then he will need to increase pump output so the 'I' value would also increase. My guess is that he would calculate the % change in flow rate for the % change in engine speed, then apply that percentage to the current pump signal output, then the difference between the current and new desired pump output would be applied to the 'I' reset value.
Basically, from the pump and hydraulic motor datasheets he can estimate the machine's shaft speed for a given engine speed and pump signal. This forms the starting point of the PID output and thus the 'I' reset value. Once the system is reset and running with the new estimated value, the PID is allowed to take over to make it more accurate.