Not entirely. Immigration courts and judges are run by the Chief Immigration Judge who is appointed by the Attorney General who works under the Executive branch. They are not part of the Judicial branch.

Immigration Court is formally known as the Executive Office of Immigration Review. This is a department within the Department of Justice. Immigration Judges are appointment by the Attorney General and are not federal judicial branch judges.

Trump has in fact ordered the immigration judges to dismiss immigration cases as soon as the lawyers them to so ICE can arrest people more quickly, and they are doing it. Well, the ones he hasn’t already fired are doing it.

Trump has his own private police force and court system.