I’m unsure about the meaing of the Provision in the second paragraph. It would appear that cession of the property was contingent upon its continued legal use. Certainly, harboring a hostile force within its walls would not be considered legal use.
What is clear is that the state usurped any individual claim to the property.
In the specific case of Fort Sumter, in 1827, Secretary of War John C. Calhoun had approved the construction of a new fort in the harbor. The first appropriations were made by Congress in 1828 and construction started on the harbor shoal. In November, 1834, after the United States had expended roughly $200,000, one Major William Laval, Esq., claimed title to the "land" which included the under-construction fort.A South Carolina statute passed in 1791 established a method by which the state disposed of its vacant lands (we tend to forget that much of the territory of the states was empty in the Nineteenth Century: in the original thirteen states, this land was held by the states; in the remaining part of the country, it was held by the Federal government, except in Texas, where the public lands were retained by the state when it was admitted). Laval used the law to claim title to the land - but he described it in a vague manner and given the lack of decent maps of any of the country, his vagueness hid the exact location of the tract he claimed.
When Laval appeared on the scene, the Corps of Engineers stopped work and asked for instructions. It appeared that Laval had filed a proper claim for the land - except that the "land" was below low tide and therefore exempt from purchase.
Well South Carolina was aghast! They did not want to lose the fort to protect themselves, nor the payrolls that would come with the completed fort.
The result was the state law ceding the land to the federal government.