Secession itself is not levying war nor is it treason against the US.
Firing on Fr. Sumpter was levying war, and those who fought against the Union were either in rebellion, or committing treason. Sorta by definition.
The hotheads of South Carolina provided a pretext for war, and the raising of armies by the other secessionist states was certainly a provocation for it.
As for the "constitutionality" of secession .... well, in essence it was a big "never mind, we don't actually mean it any more even if we did at the start." In forming its "more perfect Union," the Constitution either had actual meaning and authority, or it did not. By seceding, the Southern states denied that the Constitution had any overarching authority -- a pretty indefensible case, when you get down to it.
All that said, whether or not "states' rights" was a cause worth fighting for, the proximate cause for the South's secession -- maintenance of slavery -- was cowardly, greedy, and inhumane. The Southern soldiers were gallant and brave, but in the end -- and no matter what their personal reasons -- they were fighting to preserve a barbarous institution.