It was South Carolina property. That is moronic logic not worthy of a DP poster. It was South Carolina property before they joined the union and it was South Carolina property when they left.
If this is not true then all of it is British property. South Carolina and the U.S. stole it from England, and so the Union could not claim legitimate ownership anyway.
And no I don't think any government legitimately owns anything, but if we're discussing which government 'owns' something then the first claimant has priority.
The south didn't invade the north, the north invaded the south. The south was supplying Ft Sumter because Lincoln refused South Carolina's invitation for them to vacate Ft Sumter.
President Buchannan had an agreement with the south that they would not attack Ft Sumter or Ft Pickens if the north did not try to reinforce them.
Lincoln knew this, waited for Congress to be out of session and then sent in reinforcements. The officer ordered to reinforce Ft Pickens disobeyed the order because he thought it had to be a mistake, and would put Union soldiers at risk.
Sadly the order to reinforce Sumter was obeyed. Even so they just lobbed shells at each other as a pretense so the northern forces could surrender with honor. They did, without battle casualties, and were sent home.
Neither side killed a single person on the other side.
This was Lincoln's excuse to launch an un Constitutional war.