I think it's a fascinating question though (how asylees and refugees would vote if they could, vs immigrants and migrants), one which I don't even have a gut feeling for.

Most migrants from Central/South America will already be somewhat familiar with US culture due to geographic proximity, and often will have family and friends here who can help assimilate/absorb them into both local/municipal cultures and the broader US political landscape.

Refugees and asylees don't necessarily have that, especially if they are coming from a non-democratic and non-Western culture.

I would love to see data on this.