The OP must have had a reason for mentioning Cuba. Something with Cuba being a country the DR compares itself with as it’s similar. Another is Puerto Rico. Venezuela maybe. My country Denmark does the same with Norway and Sweden.
Cuba was wealthier and more developed than the DR, especially Havana which was often talked about in glowing terms (in a way similar how now people tend to talk about NYC though I think that has reached a peak.) Not anymore. The DR has been having some Cuban migration, but almost all were professionals and a significant amount was using the DR as a launching pad to reach Puerto Rico and then the USA. Now it seems there is a growing presence of everyday Cubans moving to the DR (at least in Santo Domingo) and they appear to be settling rather than using the country as a launching pad.
With Puerto Rico is simply a case of Puerto Rico not not doing as well economically for more than a decade while the DR has been catching up, but it's still considerably wealthier and more developed than the DR. The typical Puerto Rican that one finds living in the DR are usually in retirement age and/or with a Dominican spouse. That is not the case with Cubans. Many have a Dominican spouse and almost always they met in the DR (with Puerto Ricans there is a significant amount where they met in Puerto Rico itself or in the USA.) They appear to be younger and they specifically move to the DR for greater opportunities.
The growth of Cubans in the DR seems to be due mostly to improving conditions in the DR and, at the same time, deteriorating conditions in Cuba to the point the DR is now ahead of Cuba in most things. For Puerto Ricans improving conditions of the DR probably has made it easier to settle in the country compared to the past, especially since now there are more options. But for them the main motive isn't better job or business prospects, but a cheaper cost of living compared to Puerto Rico. Contrary to US/Canada/Europe expats which tend to have their "enclaves," Puerto Ricans tend to settle in more general Dominican neighborhoods and there isn't a single neighborhood or gated community anywhere in the DR that could be said Puerto Ricans make up a good chuck of the population. There are some gated community, especially in the north coast, where they are dominated by "gringos."