Louisiana attracted a large number of English speaking settlers after 1803 as the state was settled by an influx of English speakers grabbing up land free land so that by the 1830s French speakers were the minority. Once the land had been claimed, the state attracted few immigrants or migrants from other states, so that by 1910 around 95% of the population living in Louisiana had been born there. Despite this, a considerable minority continued to speak French as their primary language for over the next century.
By the late 19th century both Cuba and Puerto Rico were largely settled with little land available to attract a huge influx of settlers. Additionally, what few immigrants that did arrive in both islands, even after 1898 were largely from Spain, though there were Haitian labourers and Chinese were brought to Cuba during the early 20th century, both of which did not use English as a primary language. The industrial northeast and Midwest would continue to have more pull to migrants, at least until the 1960s.
Additionally, with little industry there would be few English speakers settling in the islands, or even huge numbers of foreign immigrants. For nearly a century after the Civil War, the ex-Confederacy attracted few immigrants and few migrants from other states. People tended to live and die there or leave for greener pastures. In 1910, upwards of 90% of the inhabitants of the ex-Confederacy were born in their respective states. I imagine that Cuba and Puerto Rico would be the same. The lack of air-conditioning would make the islands about as attractive as the British West Indies were to people from Britain or Canada to settle in (not very attractive at all). As a result, a small number of Americans would settle in the island to engage in business, but many would have to learn at least some Spanish. I imagine that bilingualism would become important in Cuba though, as the more educated classes would want to do business with U.S. companies. This might make Cubans in the U.S. more dispersed, instead of settling mostly in Miami and the New York area.
To get an English-speaking island, have the British conquer Cuba in 1762 and refuse to return Havana to Spain. The island did have some 140,000 inhabitants at the time of the British conquest, and Puerto Rico had some 40,000 at the time. This was the peak of the British slave-importing period, and extended rule by Britain might make the demographics of the islands look more like Trinidad or Guyana.