Ponca Dan.
My area of expertise extends quite a bit into the area of Administrative Law. When Congress passes a statute (such as the The Personal Responsibility and Work Opportunity Reconciliation Act of 1996) which is the law disallowing LEGAL immigrants from receiving public assistance for at least 5 yrs upon arrival, the Administrative Agency empowered to enforce related legal provisions, is tasked with (on a near immediate basis) rewrite its Rules to enforce these new provisions. Thus, any Administrative Agency which accepts and processes request for aid, would amend its application forms and inform all employees of the new standards for review. Thus, the Agency's rules would reflect that no application from someone not meeting the new criteria could be processed or approved. So, no legal immigrant who doesn't meet the 5 yr requirement, would be pretty much automatically rejected as the new application forms would inquire as to that issue. (BTW, it's a federal crime punishable by fine, imprisonment or both to lie on said forms.)
Administrative Agencies are kind of a "shared responsibility" set-up, with the Executive Branch and Congress having pretty much equal say over them.
I have no reason to believe, and I certainly haven't heard ANY allegations by ANY Republican/Conservative/Media outlet that this provision of the law is NOT being enforced by the Dept of Healthy and Human Services. (If it was not being enforced and given that the Republicans have had control of the House for going on 6+ yrs, and the Senate for 2+ then I would believe that they would have been raising a stink if it wasn't.) I would also note that Trump did NOT predicate his call for this duplicate legislation by making any such claim.
This is all just "theater" - I'll guarantee you that someone in the Trump hierarchy knows this (Especially with Tom Price on staff) is already law, but also knows in political terms it plays well to Trump's base. I would be surprised if one in a thousand attendees at that rally has/had any clue that this was already law. From a political standpoint, that's all that really matters to a large degree, as perception often trumps (no pun intended) reality.