How did the end of the military occupation in the south lead to the birth of 'Jim Crow' system of government?

The idea that the South was under military rule and military occupation is really a myth. The Union army was demobilized very fast at the end of the Civil War.  The assassination of Lincoln just a few days after Lee’s surrender at Appomattox enabled Radical Republicans to influence the process of Reconstruction in a manner much more punitive towards the former Confederate states, but not much of the army remained.  Some people thought they left too fast, because there was so much chaos and violence in the South. By 1866, there are 10,000, 12,000, maybe 15,000 soldiers left in the South. But most of them were in Texas, fighting the Indians. You could go for months and months in the South without ever seeing a federal soldier. There were small encampments of federal soldiers around. And if there were outbreaks of violence, they would sometimes be brought in to try to suppress it. Law and order was in the hands of governments, not of the army.  Any military rule was very brief in any practical sense.Radical Republicans believed in aggressively guaranteeing voting and other civil rights to African Americans. They clashed repeatedly with Lincoln’s successor, Andrew Johnson, over the issue of civil rights for freed slaves.

Due to the chaos of that era, it was Johnson’s attempt to regain some semblance of order that brought about the Jim Crow era.  The Compromise of 1877 is what really enabled former Confederates who controlled the Democratic Party to regain power. This is the actual beginning of the “Jim Crow Era” and began a long period in which African Americans in the South were denied the full rights of American citizenship.