Your homeonwers rates have nothing to do with FL. States set rates independently. I doubt your insurance has quadrupled over the last 2 years and is doubling again like ours in FL. You rate increases represent your risk, not ours.
Increases are controlled by the State Insurance Commissioners. Increases have to be applied for and approved by that department. This is where the wrinkle comes in. The departments of insurance are consumer advocates and generally do not allow massive increases. This means the carrier must slowly recover loss over a period of years. That sucks because investors want profit from the company now (to state the obvious, insurance is a business and that business has only one duty, make money).
If the State that kicked their butt in the last few years cannot take a deep enough increase to offset that in the next 36 months, then the carrier will have a net loss for that period when it comes to profit projections. The companies will make up that shortfall on all policies across the country to ensure the investors get the most bang for their investment. They will make up various excuses for this increase, none of which will be the hurricanes. High cost of employment, high cost of energy, property values are going up, hail, domestic water losses, litigation, mold. They have a zillion excuses to get your money.
The big boys:
Allstate
State Farm
Nationwide
Travelers
Farmers
Trust me, they will get into our pockets and they will make a profit, no matter where the hurricane strikes. It will never be written that our rates jumped from hurricanes, even if they did.