According to that article, it says both parties wanted larger government and expansion of federal power, minus democrats not wanting their slaves taken away by government. Republicans wanted bigger government power for the reason of expanding the United States, putting up railways/trade routes across the United States because it's better for business. Democrats were "conservative" in the sense they wanted to conserve their right to hold slaves. So technically Democrats were more conservative here because they wanted to keep slavery, as opposed to Republicans who were seeking to expand the United States and the trade within the country, and once that was accomplished they supported smaller government, and more conservative values because those are what is good for business.

Even still, the south remained largely democratic up until 1960ish when Barry Goldwater got the votes from these states. The reason for this is Goldwater believed it was unconstitutional for the federal government to enforce the civil rights act because the Constitution states that any power not explicitly given to the federal government went to the States. Since civil rights wasn't mentioned as a power for the federal government to give out, it should have fallen on the states. This is the reason why the democratic south voted Republican. The civil rights act was the only reason they voted Republican at that point, and eventually they started to accept more and more conservative values.

Overall, both parties in the 1880's wanted larger government for different reasons. The democratic party was only conservative in the sense they wanted to conserve their slavery-dependant lifestyle, while Republicans wanted to expand government in order to expand the United States and the business between states and then they immediately went back to smaller government and less federal power after that was accomplished. So no, they didn't really "switch platforms"