The fort belonged to the United States of America. It wasn’t their place to be evicting US troops from a US fort - politely or otherwise.
And since that territory was no longer part of the United States, and since the United States and the Confederacy didn't have a treaty concerning such forts; the presence of the Fort became a hostile military action against the Confederacy.
The rest is history.
Any people anywhere, being inclined and having the power, have the right to rise up and shake off the existing government, and form a new one that suits them better. This is a most valuable, a most sacred right—a right which, we hope and believe, is to liberate the world. Nor is this right confined to cases in which the whole people of an existing government may choose to exercise it. Any portion of such people that can may revolutionize, and make their own of so much of the territory as they inhabit.