I was reading about the Siege of Yorktown tonight and read that the Comte de Grasse sailed from the West Indies to the Chesapeake Bay, "transporting 500,000 silver pesos collected from the citizens of Havana, Cuba, to fund supplies for the siege and payroll for the Continental Army." Would these pesos be distributed directly to soldiers, or given to a central authority who would dispense local currency? If a soldier were to be given pesos, could they spend it locally or exchange it for local currency somewhere? The closest question I could find was this one, but I'm specifically interested in the Revolutionary War, given that funds were likely to be coming in from multiple countries (France, Spain) allied with the Americans.
I am unable to answer your question about how the pay would have been actually disbursed. I know that Continental soldiers were often paid in scrip and other paper currencies that became so inflated as to be worthless, though I don't know for sure if they received specie when available.
To the later question, yes, they could spend silver pesos locally. Specie, ie hard currency of gold and silver, was highly valued in this period because of its intrinsic value. Unlike paper money, which at the time was easily counterfeitable and not backed by a modern banking and financial system, specie was transferrable from place to place. A peso would be as valuable as an equal weight of equally pure silver in another denomination. Spanish currency in particular during this time was the (forgive me) gold standard in the West, since the Spanish colonies of South America produced so much of the specie then in circulation.