Short answer: hurricane season runs June through November. Locals prepare once in late spring: know your evacuation zone, stock a week of basics, photograph the house for insurance, and decide in advance what would make you leave. Then they get on with summer.
Know your zone first. Evacuation zones are published by the city and worth looking up before you ever need them. Where you live determines when you would be asked to go, and knowing it turns a stressful broadcast into a plan.
The kit is boring on purpose. Water, shelf-stable food, medications, flashlights, batteries, cash and a full gas tank when a storm enters the forecast. Most of it you already own; the work is putting it in one place in May instead of one aisle-fight in September.
Paper the house. Walk every room with your phone camera and store the photos somewhere off-site. If you ever file a claim, that ten-minute video is worth more than any memory.
Line up your people early. The roofer, the tree service and the fence company you already trust are the ones who answer after a storm. Our /directory/?cat=Home+Services category is the place to find them in the calm, and our guide on choosing a roofer covers the storm-chaser problem in detail.
Perspective, from locals. Jacksonville's position spares it the worst of many storms, and most seasons pass with watched radar and a few wet weekends. Prepare once, properly, and the season is mostly just summer.