I'd have to agree that it was illegal. The "Full Faith & Credit" Clause (Article IV, section 1) states that "the public Acts, Records, and judicial Proceedings of every other State" be given FULL (complete) credit. It does not say that if the federal government dislikes them it can refuse to recognize them ex post facto. Their
Declarations of Secession were executed within the existing laws.
Also in Article I, Section 2: "When vacancies happen in the Representation from any State, the Executive Authority thereof shall issue Writs of Election to fill such Vacancies." If the seceding state were still a member of the Union - then THAT state - and only that state - could elect replacements.