In general, it is best to transplant in the late afternoon/evening. That way, the plants have several hours of darkness and cooler temps to adjust to their new environment and lessens transplant shock. The plants should be damp prior to transplant, but not just watered. You want all the soil to stay with the roots when removing the plant from the pot. Water the plant in after you transplant to the new container. Keep the newly transplanted plants out of direct sun for a few days, giving them the opportunity to adjust. I assume you have properly hardened your plants off. If not, gradually introduce them to direct sun. Check moisture daily to figure out how often you need to water. Do not over-water.
There's several folks here that live in Florida, but I'm not one of them. Perhaps they'll add some FL-specific things to consider.
Good luck and have a great season.