The rise of Protestantism in Latin America started about the same time as Vatican II was made. I'm not sure if it was ever correlated, but it wouldn't surprise me.
I believe there is a certain narrative put out by conservatives to the effect that evangelical protestantism in Latin America came about as a reaction against left-wing developments in the RCC. But I think it also might be as simple as the long-noted trend toward protestantism among upwardly mobile capitalists, not neccessarily related directly to what was going on in their former churches at the time of conversion.
South Korea saw a big rise in protestantism in the latter half of the twentieth century, partly building on pre-existing missionary work, but also probably just because people were becoming more affluent and the gospel as preached in those churches just sort of jibed with that. Not likely a reaction against Vatican II, since I doubt most of the converts were former Catholics.
I do believe Korean protestantism was seen as a reaction, though possibly a subtle one, against the strictures of Confucianism. So there was an aspect of rebellion against the standing orthodoxy. Possibly Latin American evangelicals see protestantism as more amicable to their social aspirations than Catholicism, but now I'm kind of speculating.