We had an interesting discussion last week in Systems 122 regarding turboprop engines and when the propellers actually start rotating. It’s a function of the airflow over the turbine that drives the reduction gearbox. The C-130 gearbox adjusts the output of each engine and keeps the propellers turning in phase to minimize vibrations. This is done by adjusting the pitch using the constant speed prop for each engine. The engines actually maintain 100 percent RPM.
Here is a link for a publication discussing the C-130 powerplant and other related systems. Hope you find it useful!