Hurricane season in the Atlantic Basin (which accounts for hurricanes on the Caribbean shore of Mexico) starts June 1 and ends November 30. Maximum activity is between August and October, with the peak activity generally being in early to mid September (as determined by the U.S. National Hurricane Center). A hurricane or tropical storm can occur anytime in this period--Emily occurred in July 2005 and Wilma in October 2005. The 2005 hurricane season was the worst in 154 years. However, it was an anomaly and is not expected to be repeated soon. The vast majority of hurricanes do not make landfall. The majority of those that do reach land don't strike the Mayan Riviera.
Travelers visiting Playa at this time of year should keep a close watch on the storm warnings and consider travel insurance just to be safe.