Not quite. In treating the temporary injunction as a preliminary injunction, and therefore appealable, the Ninth accepted the reasoning of the lower court that an immediate stay of the order was necessary. The Ninth's responsibility in that case was to reassert the necessity of deference to the political branches for political decisions, and to rule that the lower court erred in issuing its injunction.
Robart should have deferred to the political branches on political matters and did not. The Ninth compounded his error by reinforcing his claim that the administration failed to establish the need for the ban. Actually, given the existing case law, that requirement fell on the plaintiff, who established neither that harm to their universities was exigent, nor in fact, that actual harm even existed.
but in no way did it somehow declare the EO to be unlawful or illegal, that issue has not yet been heard in a court of law.
I agree that technically it did not do so ... yet.
But in its decision the Court justifies its failure to issue mandamus on the basis of the likelihood that the plaintiff will prevail. And therein lies the worst reasoning of the decision. If the court really believes that: States cannot argue on behalf of their citizens but can argue on behalf of their institutions as third parties to direct harm, that there are due process protections for non-US Persons, or that there are First Amendment problems with preference to persecuted minorities (who are also not US Persons) then the handwriting is clearly on the wall.
Thank you for your excellent illumination. I take it you have some legal training?