Once they seceded it was no longer a United States military installation. It belonged to them.
This is what the entire argument hinges upon. If the principle articulated in the Declaration of Independence (our own founding document) is true, then they had a right to secede, and therefore the fort was theirs. If it is not true, our own nation is not legitimate either.
I personally believe that the Laws of Nature, and of Nature's God, grant any people anywhere the right to be free of a government they despise, and which no longer represents their interests.
So did Abraham Lincoln, twice, prior to 1860.
It did not belong to them. The Government of South Carolina ceded the land that Sumter was built on in perpetuity to the Government of the United States. The Government lived up to its obligation and built Fort Sumter.