You mean citizens of the CSA?
The whole of Lincoln's argument can be summed up in this: the States are not allowed to leave the United States.
If that were taken as true, then they must have been citizens of the United States, transitively through their citizenship in their State…
What it also means is that the Civil War was Treason, on part of the federal government due to the definition in the Constitution:Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort.