Spanish Florida and St. Augustine was such a remote outpost from the Spanish crown that it really didn't matter who was in power, because things pretty much carried on as business as usual. When Napoleon took over the Spanish crown and made Spain a constitutional government, it had little effect on St. Augustine. After a couple years when the city finally did get a new constitution, it made almost no difference. Royal appointed officials just stayed in pretty much the same positions with a new constitution.
Finally the biggest change came in 1821 when the United States gained Florida as a territory. It was not a monetary purchase as many people have been led to believe, but canceling of debts from the previous War of 1812. As far as we know, there was not any money that was actually exchanged. The Adams-Onis Treaty was the only bill of sale that was exchanged.
I wonder if Spain had thought that it would be only temporary, and the situations would change in 20 years and they would get Florida back. It was not without precedence. Territory in the New World between Spain, France, and England has been traded back and forth for the past 300 years. They may have thought that the new American republic would not survive after another generation, and would ask for the European powers to help them out with their failed experiment. But the days of a Spanish empire were waning, and the only areas they still held in the Caribbean were Cuba and Puerto Rico. 77 years later, the Americans would take even those.