One, these ads are mandated by law. Even if you are hiring people through normal modern channels like online ads, you must legally show that you placed a newspaper ad because the law is old and expects old-fashioned ads. Obviously they don't want candidates through this pipeline but that hardly means they don't want candidates!
Two, this legal requirement is for green cards / permanent residency, for a candidate already hired via H-1B or equivalent - and a green card allows immigrants to move jobs and otherwise demand a genuine market rate just as if they had generations of American blood.
I don't think this tweet was intended to be nativist propaganda - replies make it sound like he was just ill-informed - but it's still nativist propaganda.