No, it didn't. It literally did not deal with that issue at all. It only dealt with whether or not the lower court examined the issue sufficiently, and SCotUS said "no" at the level of aliens without ties.
You're quite correct: the Supreme Court did not address the issue of Trump's authority at all. The Court simply agreed to address that issue later this year, in its next term, which begins in October.
It also modified the preliminary injunction that has been preventing the Trump Administration from carrying out the executive order.
Under U.S. law, a preliminary injunction is a rather rarely granted restriction on the behavior of a party to a lawsuit that is only issued when a court determines that the adverse party (in this case, the plaintiffs who are challenging the Trump executive order) is likely to prevail when the case goes to trial.
The Supreme Court concluded that the preliminary injunction issued against the Trump Administration was excessively broad—that it could not apply to aliens who had no connection to people or institutions within the United States because the U.S. government has no jurisdiction over them. So it scaled it back.
Significantly, the Court did not lift the preliminary injunction altogether (three Justices dissented from that part of the opinion), which indicates that six Justices accepted the conclusion that the plaintiffs challenging Trump's executive order were likely to prevail at trial. At least for now.
However, as I said in an earlier post, I wouldn't infer that the Supreme Court will ultimately rule against the Trump Administration. The Justices tend to defer to lower court decisions regarding issues such as the applicability of injunctive relief until they can hear and consider full arguments.
