Corsica, a Mediterranean island, went through some significant political upheavals in the 18th century. After coming under the rule of Genoa for approximately 500 years, the people of the island spent 40 years fighting for their independence in a series of revolts, culminating in 14 years of autonomy. Corcisa was "given" to France in 1768 as part of the Treaty of Vesailles.
A former rebel leader, who had been appointed governor of Corsica by the King of France in 1790, turned the isalnd over to the English in 1794, rather than be tried for his support of the Bourbons. This Anglo-Corsican alliance only lasted for 2 years, until 1796, when the French regained control. According to an article in The Book of Trinidad, this is the time frame in which the "Corsican Immigration" to Trinidad occurred, perhaps due to nobles from Corsica island seeking a new home.
In any case, the Corscians weren't there very long before the island was taken by the English. Don Simon Agostini, a Corsican immigrant, was one of the first capitulants to take the oath of allegiance to England. The Agostini's are still a prominent family in Trinidad.
(The information on this page was obtained primarily from The Book of Trinidad, edited by Gérard A. Besson, and Bridget M. Brereton. Port-of-Spain: Paria Publishing Company Ltd., 1991.)