The flight path looks like they were approaching for the east-west runway which is pretty rarely used at Tampa so that might have caused some confusion but that's what instruments and ATC are for.

If they had to divert, St. Pete Clearwater is right there and big. They probably flew right over it. Orlando and Sarasota are also much closer than Ft. Lauderdale. Maybe they didn't want St. Pete/Clearwater or Sarasota because of weather or Southwest doesn't use them, but Orlando gets plenty of Southwest traffic.