Here is the Florida rule regarding trees
FE962/FE962: Handbook of Florida Fence and Property Law: Trees and Landowner Responsibility
"Summary
A landowner is not liable to the adjoining property owner for an alleged nuisance caused by overhanging branches and roots from a tree on his or her property; however, the adjoining property owner is legally entitled to trim back, at the adjoining owner's own expense and only up to the property line, any encroaching tree roots or branches and other vegetation that had grown onto his or her property. If the branches or roots are dead, or a dead tree falls onto the adjoining landowner's property, then the landowner of the property where the tree was originally located is responsible. If a live tree falls onto the adjoining landowner’s property, then the adjoining landowner is responsible for any damages."
Now, the Villages might be willing to do more than the law requires. Noblesse oblige may work in your favor