https://www.cbp.gov/newsroom/stats/sw-border-migration
https://www.splcenter.org/issues/immigrant-justice
Now whether these groups are actively promoting this for ideological reasons, or just trying to profit off of it is a question I am unsure of the answer.
When questioning the reasoning behind things, I find the reasoning tends to always boil down to money and greed.
Including wars - usually someone is making money somewhere and has a vested interest in keeping the war drums beating. Especially if you own an interest in both sides.
Here's some ad-hoc statistics from Columbia. Bogota [0] and Medellin [1], and I don't think the Venezuela situation needs citation.
While the stats aren't uniformly aligned, enough of the "violence"/"perception of violence" stats have increased markedly over the last 2-4 years (street robberies under [1] is a good example) to make me ask whether the migration we're seeing is a natural and emergent result from a deterioration of order in some areas of South America.
God knows if I lived there I'd have already started booking it north when hyperinflation and food riots kicked in. No need for ulterior motives there, at least.
[0] https://data.colombiareports.com/bogota-crime-security-stati... [1] https://data.colombiareports.com/medellin-crime-security-sta...