Your Post #10 is spot-on.
Yes, this is absolutely correct. What we’re seeing is 19th Century Tammany Hall tactics at work: let the immigrants in, give them free stuff, then make sure they know who gave them the free stuff when elections roll around.
Quite frankly, this is exactly what doomed the GOP with Blacks after the GOP was instrumental in passing the 1960s Civil Rights Acts. The GOP couldn’t win in a CRA vs CRA + free stuff scenario.