Yeah, states have to prove their acts to other states. Thugs grabbing a gavel and proclaiming secession doesn't qualify, I'd say. If secession was never proven then those thugs engaged in a coup and were indeed rebels.
The faith and credit required to be given to judgments does not depend on the Constitution alone. Article 4, 1, not only commands that 'full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State' but it adds 'Congress may be general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.' And Congress has exercised this power, by Act of May 26, 1790, c. 11, 28 U.S.C . 687, 28 USCA 687, which provides the manner of proof of judgments of one state in the courts of another, and specifically directs that judgments 'shall have such faith and credit given to them in every court within the United States as they have by law or usage in the courts of the State from which they are taken.'
Eh?