The Constitution had nothing to do with it after South Carolina withdrew, but you knew that.
It would still apply to the U.S. government. Sumter could not be relinquished without congressional approval.
And as I pointed out to rustbucket, eminent domain is a process governments use for acquiring private property for public use. Assuming for the sake of arguement that the southern secessions were legal, Sumter would then be the property of a foreign government. Eminent domain would not apply.