Those spots are either a fungal or bacterial disease. These are aggravated by frequent wetting. Since your tomatoes only need watering once or twice a week, I suggest you move toward that watering schedule.
As for the diseases, compost tea may help deter the disease from starting, but your County Extension Office (phone 912-462-5724) can probably recommend a more effective option since the disease already has a head start on your plants.
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