For 2010 Sumter county had reported for all ages (for a population of 98,946)
1 case of infectious syphilis
169 cases of chlamydia
64 cases of gonorrhea
Sumter county had the 64th highest rate per 100,000 citizens of STD's in the state out of 67 or only three counties were lower than Sumter.
For the years 2000 - 2010 there were either 0,1, or a maximum of 2 cases of chlamydia in persons age 55 and over in Sumter county. And the total reported cases of combined syphilis, GC, and chlamydia in Sumter country for each year has only once been 4 (2001) , once 3 (2005), twice 2, three times one, and three times zero.
You cannot break down the data to determine if the reported cases are Villagers so this is as close as I can get it. Also obviously some Villagers live in other counties. It is interesting that as the population of the Villages grew, there were not more cases being reported, and most of the newer population would be in Sumter county.
This data does not include HIV/AIDS
Florida STD Trends
So not only is the rumor wrong, the data is readily available. As noted above, if you have one case last year and 2 cases this year that is a 100% increase in the illness but not a meaningful increase.