I'd hardly call that subsidies for industry or advocacy of big government.
That is correct, and he did so because he recognized that the US could never become a manufacturing power if its fledgling industries were undersold by established British industries with the weight of the British.
The main conflict between Federalists (later Republicans) and anti-Federalists from the late 18th until the early 20th century was tariffs/trade protection vs. free trade. Trying to retroject today's political issues (and especially parties) into that debate is mostly pointless.