The only immigrant group that has had any effect on Florida elections are the Cubans, and they still vote majority Republican in state and local elections. The Mexicans and Central Americans are there, but are not registered to vote in large numbers. The main area of influx of Democratic voters has been in the Orlando area and that is because of Puerto Ricans (from both the island and NY/NJ), who are US citizens at birth.
There were folks in Palm Beach County in the 1980s that said "don't worry, we will remain Republican because all of the New Yorkers are fleeing high taxes." The opposite happenned, as people tend to bring their politics of their homestates with them.
The newer models that are fleeing, and not simply retiring as used to be the case, are a somewhat different breed.
And there are increasing numbers of them as the NE and other failed liberal states are losing their populations and inviting immigrants in as replacements, thus hastening the out-flux.
Certainly the inner cities and such are democrat infested but from what I see - and this could, I suppose, reverse - the state is becoming less of a swing state and more solidly GOP.
Certainly (hillary!) is not counting on Florida.
Look at the vote shifts in the last decade and you will see the trend.
But the general idea of folks bringing failed politics with them is disturbing.