**A single Justice rules on emergency stays. **
I didn’t know this.
I believe that each Justice is assigned a particular judicial area of the U.S. to hear requests for emergency appeals.
What has happened is simply a "stay" which stops government action until the stay is lifted. The next step in the process is for Sotomayor to bring the matter to the entire Court. It probably takes agreement from a total of four of the nine Justices to continue the stay and have the matter heard by the Court. I don't know what it would take for the Court to affirm the stay while still waiting for lower court decisions.
The Supreme Court allows itself the privilege of deciding which cases they will review and which cases will stand as decided by the lower courts. Routinely there are appeals to the Supreme Court on matters which have otherwise been finally decided by the various circuit courts of appeal. I believe that the routine appeals are handled similarly; that is, four Justices of the nine must agree to "grant cert", which means that the Supreme Court will hear the case and the case will then be decided by majority vote of the nine after they hear the case.