I doubt that either one of these post-mill groups would actually say that the Holy Spirit was not involved with the heart change, but that "their" part was either bringing forward the gospel by way of the average person or by people promoting Christ in government as well as the average person. Which would be no different than the church sending out missionaries into all the world in their way of thinking.
My personal thought is that there is a rogue element of different ideas that has joined forces with some of these different groups.
I think if we were to think of this in secular terms, then we would have to say that liberals have a real Reconstructionist post-mill mindset because they believe in big government and a type of utopia.