Therefore the question is: would their actions be lawful or unlawful? (Legal or illegal? Legitimate or illegitimate?) -- Moreover would the federal government's judgements be in line with that?
Their actions would be legal, lawful and legitimate under the Uniform Code of Military Justice if they had no knowledge that your command was unlawful.
Military discipline and effectiveness is built on the foundation of obedience to orders. Recruits are taught to obey, immediately and without question, orders from their superiors, right from day-one of boot camp.
Military members who fail to obey the lawful orders of their superiors risk serious consequences. Article 90 of the Uniform Code of Military Justice makes it a crime for a military member to WILLFULLY disobey a superior commissioned officer. Article 91 makes it a crime to WILLFULLY disobey a superior Noncommissioned or Warrant Officer. Article 92 makes it a crime to disobey any lawful order (the disobedience does not have to be “willful” under this article).
In fact, under Article 90, during times of war, a military member who willfully disobeys a superior commissioned officer can be sentenced to death.
So the men under your command should obey your orders if they have no knowledge of the fact that you “grabbed some rank” illegally. The accusation that you “grabbed some rank” is not good enough, there would need to have been an official finding to that effect.