I am not a lawyer, so I urge people to read the text and decide for themselves. Here's my analysis:
In order to issue a preliminary injuction, the plaintiffs must present a "prima facie" case, essentially, a demonstration that they can win the case under the assumption that all their factual claims are true. First the plaintiffs must demonstrate that they are likely to succeed on the merits of the case. Then they must show they would suffer "irreparable harm", necessitating the injunction. The court must then consider a "balance of hardships" - since in a preliminary injunction, both sides can claim "injury", the court must "consider the effect on each party of the granting or withholding of the requested relief". Further, the plaintiffs must demonstrate a "public interest" in the injunction.
For the "likelihood of success on the merits", the judge analysed each of the arguments:
1. Plaintiffs argue that the FLSA does not apply to the States; the judge decides it does, applying the "Garcia" analysis from the Supreme Court.
2. Plaintiffs argue that Chevron deference does not apply for this case, judge agrees. Chevron deference is a legal standard roughly saying that in the case of an ambiguous law, the Court should defer to the interpretation of the government body authorized to apply the law(as they are presumed experts in the field), as long as the interpretation does not contradict the evident intentions of the law.
3. Plaintiffs argue that the automatic update mechanism of the Final Rule violates the APA. The judge does not analyse this, using his previous analysis of Chevron deference to conclude that the Final Rule is unlawful and that 3) does not need to be settled.
The rest of the analysis("irreparable harm" etc) from the judge is not as long so I don't feel it's worth summarizing in any way.
I don't find the judge "making up" any law in their analysis - can you please be more specific which part of his analysis you disagree with?