Without a precedent to establish that a Tweet was a legitimate communications channel, I would not blindly have accepted such an order. The officer in command has a duty to issue his orders in a way that those being ordered can be confident of who is being ordered, who is issuing the order, and sufficient specificity as to what the order entails.
If Trump's pardon, which should have been in writing, fails to specify the scope of the pardon, then Trump is not being served well by his staff.
There is a concept called "chain of command". For example, a low-ranking soldier is expected to bring issues to his direct supervisor. To take issues to a higher level in the command is frowned upon and might be taken as lack of respect.
When I trained in the expectations for performing guard duty we were told a story of a soldier on guard duty who was approached by a Colonel who insisted that the soldier allow him to enter the building being guarded. The soldier followed his explicit orders and delivered a vertical butt stroke which broke the officer's jaw.
For his own protection by virtue of the ban on double jeopardy, the soldier was quickly court-martialed, found not guilty, and was presented with a carton of cigarettes. The order from the Colonel was determined to be an unlawful order.
A similar expectation would exist in the opposite direction. Those high up in command would typically be expected to deliver their orders down the chain of command. Again, Trump's staff should be expected to know these kinds of things and keep Trump from appearing un-military when he is exercising his authority as Commander-in-Chief.
Politically, I have decided that Trump is a verbal magician. Like a magician conducts himself so that you are always looking at the wrong hand, Trump has a way of creating small to medium level controversies that keep his opposition busy responding to irrelevancies.
What is most relevant today is the appointment of judges. Trump is having a generational effect of our courts. If Ginsburg retires, then her replacement is of incredible consequence. Whether Trump understands the protocol of issuing orders relative to a pardoned soldier is of very little importance compared to the makeup of the Supreme Court.
In this case, yes, but it might only take minutes to verify it was a lawful order.
The latest shiny object.