Miami-Dade County is about 82% Latino or African American. The Cuban community is huge, 34% of 2.5 million people is 800,000+ - a large conservative voter potential after you subtract out the children. This huge block of voters has shaped Cuban-American foreign policy since the 1950s. It's difficult to live in South Florida without learning about 20th century Cuban history. It's bloody.
The Cuban community used to be homogenous in their attitude toward Cuba, largely shaped by what the community viewed as a debacle (epic failure) of the Bay of Pigs Invasion where 68 Cuban exiles died in the 3 days of fighting or executed after capture. As far as the exiles were concerned, The Cuban Missile Crisis would never have occurred had they been successful at the Bay of Pigs Invasion. Many of my Cuban American students have explained the exile rationale in this way: JFK blew it. JFK is a Democrat. I'm a Republican. The party loyalty born of that rationale shapes elections, but that ideology is changing. Both younger and later immigrants don't hold with the hard and fast attitudes of older/earlier Cuban immigrants. The number of Cuban American Democrats is increasing along with 69% wanting relaxed travel restrictions to Cuba, less support for the Cuban embargo (52% oppose the embargo) and 68% desire re-established diplomatic relations between the U.S. and Cuba. Despite these changes, a 63% majority still thinks Cuba should retain it's designation of being sponsor of terrorism.
You might wonder why anyone would care about one group of people. It's because as a voting group, Cuban Americans influence elections in Miami-Dade County, Florida. It's hard to elect more and better Democrats to office in Miami-Dade without getting some Cuban American votes.
The Cuban American Community that came to the U.S. in the 1950s were largely middle class who were not going to do well under Fulgencio Batista and later people left in droves after the Castros took over for similar reasons. The ethnic breakdown of Miami-Dade County is something like 64% Hispanic and 34% Cuban American. That is ten times the number of Cubans estimated to live in both the Los Angles and the tri-state NYC areas. This is a voting block that in the past was largely Republican, socially conservative and easy to target for political messaging.
The shift in attitude is documented in a long term series of polls.