Chances of being caught in a hurricane
The hurricane season in the Caribbean is from June through November, with September historically being the peak month for the storms. There are exceptions.

Hurricanes are rare events. The DR has been hit by 11 hurricanes in almost 80 years. Historically, big hurricanes have been widely spaced out through the years and for the most part have hit the less populated southwestern and western coasts of the Dominican Republic.

Past recorded hurricanes that have hit the DR:

Jeanne. (Category 1). 17 September 2004. East coast, Samana on the Northeast and North Coast (as tropical storm).
Georges. (Category 3). 22 September 1998. La Romana to Santo Domingo on the southern coast.
Hortense. (Category 3). 10 September 1996. East coast from Punta Cana to Samana. 130 kph.
Gilbert. (Category 3). 11 September 1988. Barahona on the southwestern coast, with winds of 200 kph.
Emely. (Category 4). 22 September 1987. Bani on the southwestern coast, winds of 220 kph.
David. (Category 4-5). 31 August 1979. Santo Domingo on the southcentral coast to the southwest.
Beulah. (Category 4). 10-11 September 1967. Barahona on the western coast with winds of 225 kms per hour.
Ines. (Category 4). 29 September 1966. Barahona on the western coast, winds of 240 kph.
Edith. (Category 2). 26-27 September 1963. La Romana on the southeastern coast, winds of 160 kph.
Katie. (Category 1). 16 October 1955. Barahona on the western coast, winds of 125 kph.
San Zenon. (Category 4-5). 3 September 1930. Santo Domingo on the southcentral coast.

Note that the last hurricane to hit the capital city of Santo Domingo was Georges (Category 3) on 22 September 1998 and before that, Hurricane David (Category 4) in 1979 and San Zenon, Category 4-5 (September 1930). Thus the likelihood of you being caught in one is very small.

Check out the hurricane probabilities in the DR!