Let me tell you this: No too long ago in history, Dominican passport holders could enter not only Mexico, but pretty much ALL countries in LA visa free or visa issued at arrival.
What changed the policies came on the heels of how the OAS responded to the Trujillo regime after the attempts against some people outside of the country (RD).
Back in those days the DR had a formidable net of spies and agents (many non-Dominican) on the payroll of the Dom. Gov.
Once the first limitations were imposed on the regime, one of those was the requirement of visas to those countries previously open to DR passport holders. This included NATO states as a follow up on the request of the U.S. and other non-NATO nations.
The DR passport was back in those days almost better than having a U.S. passport. In fact, the DR passport was BLUE!
Once the regime was down and done with, the U.S. lifted most of the limitations for visas issued to Dominicans, but the other countries didn't follow much due to how things were not so good on their own soils.
To speed this, the U.S. requested to those nations that Dominican passport holders with a U.S. visa stamped on it should be allowed visa free in those nations and they did comply. The U.S. then went on a give-away spree of visas for Dominican passport holders. They had two consular offices (one in SD and the other in Santiago) issuing visas like hotcakes on request.
Thing was that most Dominicans that could afford the costs of travel to other countries turned their vacations and shopping sprees to Europe and other places more welcoming of their extended families. Sans the trouble of visas before hand.
By the time the U.S. got smart, the bulk of visas issued in the Santiago consulate went to campesinos.
Other countries have started to see the DR as a potential economic tourists source for their economies as well. The DR is a upper middle income country and growing year on year.
More two tenths of the DR born population holds U.S. or other foreign nationality or permanent residency. A greater number holds multiple entry visas for the U.S and other nations.
This will all change step by step, country by country.