The CSA was not even created before the states seceded. Consider the order of secession:
South Carolina, Convention passed Ordinance of Secession, 20 Dec 1860
Mississippi, Convention passed Ordinance of Secession, 9 Jan 1861
Florida, Convention passed Ordinance of Secession, 10 Jan 1861
Alabama, Convention passed Ordinance of Secession, 11 Jan 1861
Georgia, Convention passed Ordinance of Secession, 19 Jan 1861
Louisiana, Convention passed Ordinance of Secession, 26 Jan 1861
Texas, Convention passed Ordinance of Secession, 1 Feb 1861 (admitted to CSA 23 Feb)
Constitution of the Confederate States of America signed 11 March 1861
Virginia, Arkansas, North Carolina, Tennessee, Missouri, and Kentucky were admitted between 4 April - 10 December 1861 (after Lincoln's call for troops).
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Pray tell, how can a state exercise powers that it is specifically prohibited from exercising?
The real question we should be asking is how can the federal government assume rights not specifically delegated to it?
Impossible and invalid in US law.
An ordinance or act of secession is a "thing" in the laws of a state which is clearly blocked by the Supremacy clause.
The Judiciary Act of 1789 requires that controversies between the states be submitted to the Supreme Court.
Read it and weep.
Walt