Only during hurricane season is when you have to be really aware of the weather here. Hurricane season starts in June and ends the last day of November. Even then hurricanes have appeared in the Atlantic Ocean before June and after November. You do not have to worry too much because the probability of a hurricane to hit the Dominican Republic is low. In 80 years the Dominican Republic has been hit by 11 hurricanes. They are Jeanne, Georges, Hortense, Gilbert, Emily, David, Beulah, Ines, Edith, Katie, and San Zenon. These hurricanes have hit the Dominican Republic between the months of August and October. September is the most dangerous month in respect to hurricanes. Of the 11 hurricanes that have affected the Dominican Republic 9 have been on September.
One of them hit on August and the other one hit on October. One detail to notice this is the count for hurricanes only; there are tropical systems of less intensity like tropical storms and tropical depressions that have hit the Dominican Republic with more frequency. Tropical storms have hit the Dominican Republic outside hurricane season like the case of tropical storm Olga that hit on December. Even when tropical storms are not as powerful as hurricanes they still have to be considered as a threat. Most of the resorts on the island are prepared to act in case of any tropical system that might hit the island. Since the experience of the past hurricanes they have installed underground phone lines and prepared the infrastructure better to withstand the impact.
In most cases the resort management will send you to another resort far from the main affected area to spend the rest of your vacation. Still the probability of one system to hit the island in the moment that are vacationing there is quite low. The best measure to avoid any tropical inconvenience is to travel after October or before August. This way your vacation has an extreme low chance of being ruined by a storm.