they don't sound West Indian because Dominicans don't have that Southern Irish flavored dialect that West Indian islands recieved in the 17th and 18th century
but they do sound different from other Hispanics, sounds like a mix between Hispanic and West Indian
in whatever case it may be, iv comed acroos many Dominicans that have this distinct way of Speaking English, even the one's that immitate it from Americans still somewhat have this Caribbean accent in English, but PR and Cuba don't
Central American Caribbean Coastal English does not count because they are descendants of West Indians who came sometime between 100 to 300 years ago (already speaking English dialect) and have retained it but are losing their dialects slowly.
This Dominican (from Dominican Republic) immigrant in St Kitts and Nevis has a West Indian English accent, but this is explaineable since he picked his English probably there, but there's alot of Dominicans that talk like that that i personally know (skip to 15:50)
[video=youtube;9KLuYJoU71A]https://www.youtube.com/watch?v=9KLuYJoU71A[/video]