"Suburbs" didn't swing towards Clinton. Wealthy, highly educated and economically dynamic suburbs, especially those that are relatively young, swung towards Clinton. Pasco and Pinellas Counties are none of these. They're mid-market, low-education areas heavy on elderly voters with little economic vitality beyond the servicing of retirees. Also, both are heavily white (especially, in the case of Pinellas County, for a county that contains a mid-sized city with a large minority population).
Ahh, I wasn't aware they were lower education areas.