Team Logo. The Tampa Tarpons were a team in the Florida State League. They were the High-A affiliate of the Cincinnati Reds. In 1988 they moved and became the Sarasota White Sox. Retrieved from "https://prosportsteams.fandom.com/wiki/Tampa_Tarpons?oldid=8531" Categories: Former FSL Teams Teams in Florida Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.