Follow-up question. How did the military enforcing the order on US soil not violate posse comitatus?

The Posse Comitatus Act generally prohibits the use of the military to enforce domestic civil laws. I don't know if it were ever argued, but I imagine the defense would be that the order was a wartime defense measure, not domestic civil law enforcement, and thus it was appropriate to use the military to enforce it. Generally, domestic military activities that are taken to support a military purpose do not fall within the Act's prohibitions:

The Armed Forces, when in performance of their military responsibilities, are beyond the reach of the Posse Comitatus Act and its statutory and regulatory supplements. Analysis of constitutional or statutory exceptions is unnecessary in such cases. The original debates make it clear that the act was designed to prevent use of the Armed Forces to execute civilian law. Congress did not intend to limit the authority of the Army to perform its military duties.

sgp.fas.org: PDF document

That said, I don't know for sure if the military ever did enforce it. Fred Korematsu (of Korematsu v. U.S.) was arrested by the FBI, and Gordon Hirabayashi (who was convicted for violating the curfew before it was converted into internment) voluntarily turned himself in to the FBI in order to test the legality of the law. The EO and the military might have established the curfew and the exclusion zones, but it might not have been the military itself that actually enforced it against non-compliers.