Money is fungible, if the Successor States were paying taxes, then that money was used to fund the Star League, including terraforming. I doubt they had a payroll tax for terraforming alone, just income taxes, tarrifs, etc going into a general fund, much like governments today.
In the US, people in NY are paying for roads in S Dakota and Vice Versa. It is all one giant pot of money the source is inconsequential.