This "amnesty program" as you call it, was deferred deportation by Obama EO, since no way would the GOP majority congress approve it permanently. It WAS presented to Trump.
One day it was described as pertaining to 800,000 but it morphed to 3.6 million, and grew from only deferred deportation, to chain migration etc.
It's not 'as I call it.' Regardless of circumstances, they're here illegally. The program allows for a permit to stay and review as to whether you'll eventually leave or be allowed to remain, have a path to citizenship, and jump the line ahead of other legal applicants. Amnesty is the forgiveness of past legal transgressions. You can't honestly say it's anything else, whether it's applied to 800K or 3.6M.
Of course it's grown to chain migration. We've seen this before when it was called the Family Fairness Program in 1987. A really bad idea then has become an absolutely terrible one now. Admittedly, Deferred Action for Childhood Arrivals has a much better sound and flow than the You Won't Be Deported Until We Figure Out How To Make You Citizens, Then We Won't Deport You Act.