This is an excellent question. I think it would be appropriate to outline the administrative districts for a moment. You are right that in the first two decades of the 19th century Florida was under the jurisdiction of the Vice Royalty of New Spain. This designation, however, does not mean that it shared the same cultural, economic, social, or political problems. When the Spanish Crown first began to consolidate power in the early 16th century, they created the Audiencia of Santo Domingo. These court systems were the foundation for political and legal control in the region. Overtime, the Santo Domingo courts could no longer govern effectively and additional audiencias were created. Overtime and through trial and error, the Spanish Crown realized that it needed greater political control. This led to the creation of the Viceroyalties of New Spain and Peru. Still, political and economic control did not mean that each viceroyalty’s dominion was homogeneous. New Spain had power over the Caribbean but also Central America and California, areas that were not alike. Peru controlled the Andes, but those areas were just as diverse geographically as they were demographically. Curiously, Venezuela was not put into a viceregal unit until the early 18th century, when it was removed from the jurisdiction of the Audiencia of Santo Domingo. This is a long way of saying that the viceregal state and its subjects were never on the same page at the same time.
Working to limit Creek trade networks and Spanish control in the western part of the colony, President Thomas Jefferson and his administration worked for years to subvert Spanish control in the region. Some of his antics would no doubt have fit right in with American foreign policy ideas in the 1970s and 1980s in Latin America. Jefferson urged the Governor of New Orleans to send in bandits and irregular militia into Spanish areas of Biloxi and Mobile. This drew Spanish security forces away from Pensacola and the Creek frontier and disrupted trade and settlement. American ships even worked with British Royal Navy vessels to capture Spanish and even Creek-controlled shipping, which the Americans would then buy off the British and press them into American coastal service. Despite his best efforts, Jefferson was unable to provoke the Spanish colonial or royal authorities into a war, but he certainly tried. Unfortunately for Jefferson, colonial Florida in the 1800-1820 period was perhaps the freest place in North America. Religiously, Catholics were free to settle in the area but protestants were not prevented from settling in the Spanish colony as long as their services were not advertised. Taxes and trade benefits were better in Pensacola and St. Augustine than in New Orleans and Charleston. Land was virtually free to any settler that wanted it and promised to serve the Spanish Crown and pay their low taxes. Spanish authorities attracted a few thousand American citizens after the war who took advantage of the land and financial freedoms. Most of them settled alongside former British subjects who had no rebelled during the war and had not evacuated the colony once the Spanish took control in the 1780s. In the east, the situation was similar. Spanish authorities ruled over a mixture of Spanish, British, and American subjects who moved or stayed in the area after the war to take advantage of the economic climate.
With the rebellion led by Hidalgo, central and southern New Spain were clearly in the middle of a major conflict zone. Northern New Spain and California, as well as what is now Central America, were not as active in what was clearly at first an indigenous uprising in a specific area. Florida fell into a similar predicament. What did they care if the indigenous peoples of central New Spain marched on Mexico City? Spanish relations with the Creek nation were on a slightly more equal footing than with the indios of New Spain. By the time Morelos died in New Spain in 1815, American expansion into the Florida colony included Mobile and they even occupied a fort north of St. Augustine. Finally, after American raids into the colony hunting down Seminole and Creek forces, the “accidental” capture of Pensacola and the panhandle by Jackson in 1817, and the understanding that the US would ignore territory belonging to New Spain proper, the Spanish ceded Florida in 1819. Royal authorities in New Spain negotiated a treaty with rebels there signaling the end of the Mexican Wars of Independence in early 1821. Florida became an official possession of the US a few months after that.
So to answer your question more briefly, Florida’s political, economic, and social makeup was so different than New Spain’s that locals in Florida were not bothered by social and political unrest there. Once the revolt became something larger than an indigenous uprising, the Florida colony was still not in a position to help in any way nor did it have the ability to so if they did. Once the Mexican state was created in the 1820-21 period, Spanish Florida was no longer an entity that Mexico could claim.
J. A. Brown, “Panton, Leslie and Company Indian Traders of Pensacola and St. Augustine” in FHQ, Vol. 37, No. 3/4 (Jan. -Apr. 1959).
L.N. McAlister, “Pensacola during the Second Spanish Period” in FHQ, Vol. 37, No. 3/4 (Jan. - Apr. 1959).
David H. White, “The Forbes Company in Spanish Florida, 1801-1806” in FHQ, Vol. 52, No. 3 (Jan. 1974).
Gilbert C. Din, “A Troubled Seven Years: Spanish Reactions to American Claims and Aggression in “West Florida,” 1803-1810” in Louisiana History, Vol. 59, No. 4 (Fall 2018), pp. 409-452
Peter Zahendra, “Spanish West Florida” PhD diss., (University of Michigan, 1976).