The Erie and Lackawanna each operated their own ferry services: the Erie from Jersey City to Chambers St., Christopher St., and 23rd St., Manhattan, and the DL&W from Hoboken to Barclay, Christopher, and 23rd Sts. The through fare to or from New York included the ferry trip. In addition, many railroads had passenger agents meeting incoming ships, equipped to sell tickets over their respective railroads. I think what it comes down to in this case is the question of how the tickets were provided to the travelers, beginning with the process by which the farmer in Illinois paid their fares. Presumably they would not have had the cash on them upon arrival; were they provided with some kind of voucher, which would have specified the railroad? Perhaps there was a German-American fraternal organization; there were many such, which provided support to newly arriving immigrants--could things have been arranged through the organization? I don't suppose its possible now to determine details like that unless someone recorded them at the time, but it's almost certain that whoever paid the piper called the route.