See
DR1 - Weather for general information on weather in the DR. Then see
DR1 - Hurricanes for specific information on hurricanes in the DR.
While September is the peak month for hurricanes (RAIN) in the DR, note that there have been 11 in 80 years. And those have been spread out in different parts of this very big Caribbean island.
Regarding traveling to the DR in September, go for it. The rates are great, the resorts are not packed, and the weather is no longer as hot as in July and August.
Regarding rain, given the changing climate, you could encounter several days of rain any time of the year. My experience is that regardless of the storms that may be in the area, it doesn't rain more in September than in any other month. As you say, there is rain and there is RAIN. The likelihood of you getting caught in RAIN is not high, so I would be more concerned with bringing sun tan lotion than with bringing an umbrella.
