The rate of application of pitch is usually controlled by a pitch rate controller for each hub system. The rate of application and reduction on some systems can be set individually with a small potentiometer in the electronic systems cabinet, or, if it an older system with pneumatic controls, the application rate is set using pitch rate restrictors.
The pitch application rate for each type of vessel will be different (except maybe for sister ships), and will depend on the size of the hubs, the area of the blades, the hub servo piston diameter, the hydraulic pressures involved, and the main factor will be the type of engine(s), the drive system (diesel-electric, geared diesel, or gas turbine), how many engines are running, and whether the shaft is operated in the combinator mode, the constant-speed mode, or is switchable between both modes like the ship I have just come off last week.
However, the pitch change when testing the gear (ie, with the shaft stationary) can be as little as 10-15 seconds from Full Astern to Full Ahead, mainly because the application rate controllers on a lot of installations are not looped in the pitch control circuit until the shaft rotation is actually started. If the maximum pitch application rate was available when the shafts are rotating, the sudden application of pitch can easily be enough to stall the engines and cause overload trips and auto shutdowns - not a very nice occurrence, especially if the ships electrical power is being supplied from a shaft alternator.
Cheers
Skilly