Or perhaps the definition of 'unilateral' in the English-Confederate/Confederate-English dictionary is different?
There were 11 states in the Confederacy, therefore it was not unilateral.
So yes, South Carolina's secession was unilateral, after which it became a plurality of states.
Definition of PLURALITY 1 : the state of being plural : the state of being numerous : a large number or quantity 2: pluralism 1; also : a benefice held by pluralism 3 : a number greater than another : an excess of votes over those cast for an opposing candidate