No, it doesn't. The Civil War was fought between two military units, not two police forces. When the Japanese were bombing Pearl Harbor they were engaged by the Navy, not by the Harbor Police.
The enlistment oath:
I, (NAME), do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed.
How would they engage domestic enemies if it were all a police matter?
Well, when this invasion force arrives, I hope they have taught the troops how to deal with units like these. For example, we already know not to lead the women and children so much from the movies. But these are going to be tired malnourished women and children that have marched hundreds of miles. They need to be trained not to lead them much at all.