The Army couldn't be called in without an act of Congress because of the 1877 Posse Comitatus Act, which specifically forbids the army from being used to enforce federal law domestically without congressional approval. This law was passed in 1877 to address southern concerns about federal troops after the civil war and not updated until after WWII. The Marine Corps is not mentioned by the act, which refers specifically to the "Army of the United States." Of course, the Marines have generally followed the spirit of the act, but they were not technically bound by it.

Other Federal Law enforcement agencies were practically non-existant at the time. The Secret Service and FBI were small, the U.S. Marshalls service was already committed to other roles and the postal inspectors lacked the manpower.

That left the Marines. Since they had expeditionary forces in readiness, they could muster 2000 or so troops on short notice. They had two brief deployments in 1921 and again in 1926 until more permanent mail security arrangements could be organized.

To be clear, the reference to "post" in a Marine's first general order for sentries refers to the place where the Marine has been told to do sentry duty. It is not a reference to "post" as in the U.S. Postal Service. Accordingly, the first sentence in OP's question has no relevance to the second and third sentences.