It's not exactly "visa on arrival". For citizens of the Dominican Republic, the entry requirements are the same as US Citizens: Passport valid for at least 6 months from arrival and a tourist card. The tourist card must be purchased before arriving in Cuba. They can be purchased at the departing airport from Cubana or from the travel agency that sold you the flight/package. You will need to have one before boarding the aircraft. Note that the only people who can enter Cuba with a tourist card are bona fide tourists. If you are coming for any other reason (journalism, study, diplomatic, etc.) you must have a visa.
As a US citizen, you will most likely be questioned by Cuban Immigration about your visit a little more than others. This always happens to me. They always seem to be pariculary interested in finding out my occupation at home. It mostly goes like this:
"What is the puropse of your trip to Cuba?"
"Have you been here before?"
"Do you know anybody living in Cuba?"
"Where do you live now?" "What is your occupation?" "What cities will you be visitng and where will you be staying.? "Show me proof of hotel confirmation, please."
This scenario happens all the time to me but they are always polite and friendly about it. Of course, as a US citizen, I have never been to any other country where I was questioned by immigration so much before entering.