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Before the first US Mint established the late 1790's, the matter of legal currency in the new nation was left entirely up to the states. As a result, many states had their own currency.
Amongst the general public, the most popular form of currency in use was the Spanish Piece of Eight (aka: Dollar). When the Federal Government finally started minting their own coins, they were made the same size, and out of the same materials, as the Spanish Dollar. Mexico did the same with their pesos. As a result, all three were circulated as currency interchangably until 1857.
So most likely, all government employees were paid in Pieces of Eight, or one of the currently circulating monetary equivalents.