Don't know about Russia but in South America it started thanks to several factors.

First of all due to the immigration policies pushed by most Latin-American countries in the late 19th Century. Following some 'scientific' doctrines of the time and under the idea of 'improve the indigenous race' of their respective countries, they started pursuing some policies which would make them attractive to foreign (mainly European) immigration. This created a considerable influx of European nationals (mainly Italian and German, though some French also joined in) and created communities in which some of the European ideologies were copied/divulged. The case of Argentina is particularly important as the German community which had emigrated there in the late 19th century and early 20th century kept a close tabs on what was happening in Germany and began divulging the doctrines pushed by the Nazy party. These ideologies became so powerful in Argentina to the point that one of the biggest (if not the biggest) Nazi rally outside of German soil was conducted in Luna Park in Buenos Aires and boasted a stupidly high number of attendants.

The second factor is due to a ideological affinity between the Nazi regime and a considerable sector of contemporary Latin American politics. Several countries in the region had strong far-right political sectors which saw in these ideologies a way to counter the threat that leftist organisations were posing for the established social order. Argentina again plays a significant role in this ideological connection as, aside from the previous Nazi rally, one of the prominent political figures of the time, General Juan Domingo Peron (who would then become president/dictator/economic nightmare) was heavily associated with the Third Reich (see the Blue Book in Argentina by US ambassador Spruille Braden)

This ideological affinity led to a considerable amount of Nazi officials fleeing to these Latin American countries as, given the presence of German/Italian communities and strong ideological ties with the political class, they saw in these territories a haven where they could safely hid from the persecution in the aftermath of the war. This was also helped by the fact that US government saw some of these Nazi officials as assets and actively helped their escape to Latin America in order to use them in their fight against the dangers of communism and socialism (i.e.: Klaus Barbie). Given as, barred some notably exceptions, their presence in society was open and Nazism was an enemy of the leftist ideologies which had become the enemy in the post war era, Nazism and Fascism continued to permeate sectors of society. Former Nazi officials served as bodyguards of dictators, gun dealers, smugglers, consultants etc...

Finally, and this is more of a personal opinion on the matter, some sectors of the population in Latin America have sort of lacked... Identity? Basically, these sectors have always thought that Europe (or the US depending on which country you locate yourself) has always had a cultural supremacy and that, rather than keep/preserve our traditional culture and practices, we should discard them and copy whatever is going on in Europe/US (Europe BUT NOT Spain). This is why you see some people claiming to be European (despite the fact that they are born 6000 miles away from the place), why you see cities almost built to resemble Prague, Viena, Paris etc., and why the political elites tend to act in a manner resembling European aristocracy (though this last one has also a lot to do with our independence from Spain)