The secessions were unlawful. After all, when the Northern states were compelled to return fugitive slaves to the South, that was done on the basis of text in the Constitution that was binding on all of the states (namely, about returning those fleeing from bondage to their masters).

In fact the Constitution included many regulations and prohibitions regarding the power of individual states, so it can't be claimed that the Constitution wasn't the ultimate arbiter of power within the federal framework of government.

So with that in mind a unilateral decision by a single state to change the Constitutional government for all of the states can hardly have been legal. And even the parts of the Constitution talking about the territorial integrity of a single state all include the clause the Congress must approve the change in addition to the state itself.

If a state really wanted to secede it would have to have come up with some legal procedure at the national level from which to even make that change possible. Probably by using the Constitutional Amendment process (which is, after all, the built-in designed mechanism for altering the federal framework of government).