Construction during 1858 and 1859 was minimal due to lack of funds. It had taken over 10 years and $500,000 to complete the island. It took another 10 years and another $500,000 to complete the fort.
In November of 1860, about 150 masons from Baltimore arrived at Fort Sumter to complete the masonry work.
In December of 1860, While the outer fort was complete, only about 80 % of the interior work and the mounting of guns had been completed. Of the 135 guns planned for the gun rooms and the open parapet, only 15 had been mounted.
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"Resolved, That this state do cede to the United States, all the right, title and claim of South Carolina to the site of Fort Sumter and the requisite quantity of adjacent territory, ..."
In short, South Carolina gave up all of their rights and claims to the site (which was under water at low tide anyway) in their desire to have the US government build/maintain a fort there. They did the same with their rights to property for Castle Pinckney, Fort Moultrie, and the Charleston Arsenal in order to get the Federal government to own them.
Giving up All their Claims also means that any prior conditions are now "voided", unless included in the Final Deed, which as can be seen above, excluded any and all claims.
Also, once they gave up all rights, the Federal Government could have workmen or troops, on site at their pleasure, not at the pleasure of the state the Federal Property occupied.