The news feed I’ve read is they came via SA (Venezuela, Brazil) and Central America & Mexico. Long journeys, many lasting months or years to get to this current border situation.
Many Cubans follow that route too to get to the USA, particularly flying from Havana to Ecuador and then trekking to the US-Mexico border.
I think the route via SA of Haitian illegal immigration to the USA is here to stay. Once the genie is out of the lamp and see what is out there, it’s very difficult to get it back into the lamp!
At the very least, many of these Haitians deported from the USA will either attempt to reach the USA again or attempt to go and stay in any of the countries along the way. They know how cities are in Haiti and they’ve seen cities in Ecuador, Colombia, Panama, Mexico, etc. They have seen the difference in person and can compare.