If you're listening to the audiobooks, the narrator change can signal a different 'era' of Marple. Some narrators do the early books, others the later. That audible shift can informally group the books for you, with 'A Caribbean Mystery' falling into a certain vocal style.
The very fact that it's a 'mystery' in the travel brochure sense is key. People go there for adventure, for the unknown. The murderer uses that expectation as cover. Miss Marple subverts it. She shows that the real mystery isn't in the exotic location or the local legends; it's in the human heart, which is the same everywhere. Her method demystifies the exotic, bringing the darkness back into the familiar, understandable realm of human failing.
The heat, the sea, the relaxed resort atmosphere... it all lulls the reader and the characters into a false sense of security. Having the familiar, dependable presence of Sir Henry Clithering arrive feels like a cool glass of water—a return to solid ground and methodical thinking amidst the tropical chaos.
Honestly, it's a bit of a trope—the person who knows too much gets killed. But Christie makes it feel fresh by making the 'person who knows' such a blowhard, and the detective such a passive observer. Miss Marple isn't chasing the truth; the truth crashes into her veranda chair.
She learns of the murder by being collateral damage in the information war. The major was the target; she was just in the splash zone. But her mind is the only thing that gets stained by the splash, and that stain is the knowledge of what really happened.