Two points - secession is not a public act - it is a sovereign act of the people of the state. Public acts are those done by state legislatures and/or other state officials ["the suit concerns the public acts of an officer of the State government", Osborn v. Bank Of United States, 9 Wheat. 738 (22 US) (1824); "the public acts of public officers purporting to be exercised in an official capacity and by public authority", United States v. Arredondo, 6 Pet. 691 (31 US) (1832)]
The Effects Clause states, "[a]nd the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof."
Not "must", but may. Congress has already enacted the applicable laws.