Which event marked the beginning of Spanish control over the Cayman Islands?

The Treaty of Madrid is the correct answer as it marked the official recognition of Spanish sovereignty over territories in the Caribbean, including the Cayman Islands. Signed in 1670, this treaty was part of a broader effort by Spain to assert control over islands and lands that were previously claimed by other European powers.

Prior to this event, Spanish explorers had discovered the Cayman Islands in the 15th century, but the formal acknowledgment of Spanish control through the treaty solidified their claim. The treaty also established certain boundaries and regulated interactions between Spain and other colonial powers, further reinforcing Spain's dominion in the region.

In contrast, the other treaties listed either pertain to different historical contexts or deal with territories outside the scope of the Cayman Islands' early governance. The Treaty of Paris, for example, is more associated with the end of the American Revolutionary War, while the Treaty of Versailles is primarily tied to the conclusion of World War I. The Treaty of Tordesillas, while relevant to colonial claims in the Americas, was earlier in history and dealt with the division of newly discovered lands between Spain and Portugal, not specifically the Cayman Islands.