Government land, but why would it be Confederate government's land? I'm not entirely sure that. Even if one were to concede the legality of secession under a theory of States retaining their sovereignty, I don't know why they're entitled to land given up to the federal government. Virginia isn't entitled to Kentucky, Ohio, Indiana, etc. because they gave up this land.
The Union invaded the South because they had the better army that was capable of doing this. They did this after the Confederates opened fire. The Confederacy did invade the north. Notably twice on the east coast (Antietam and Gettysburg), but plenty of times with guerrilla warfare in Kansas and Missouri. I'm not sure why military success makes someone an aggressor. In World War II, the US wasn't an aggressor just because they were successful with island hopping against Japan.