First Federal Withholding of Funds to States?

This is actually two questions.
When did the federal government start subsidizing state funds.
When did the federal government first require a state to pass a law in order to receive funds?

In 1790, when the federal government assumed debts that states had incurred during the Revolutionary War period.

Most federal aid to states in the Nineteenth Century took the form of “land grants” rather than direct cash appropriations, and these grants were often conditional on states taking certain actions or passing certain laws. The best known land-grant law was the Morrill Act of 1862, which granted federal land (effectively, money) to the states for the purposes of building and operating universities.

As you can see within the text of the act, the grants were loaded with strings; the act lists seven conditions states had to meet in the form of laws which had to be passed, actions which states were required to take, or actions states were forbidden from taking.

Earlier examples could be cited. Consider the text of law admitting the State of Alabama to the Union in 1819. It provides:

Provided, however:

Federal funds, federal strings . . . not a new concept.