baggage: if DL accepts your bag at TPA and checks it through, DL is responsible to get it to VS at JFK and VS is responsible to get it to LHR (and thence to you if it's delayed for any reason)
you: DL **may** issue your VS boarding pass, but as far as they're concerned you're only going to JFK, and they have no responsibility to protect you onward to LHR if the TPA-JFK flight is delayed ... similarly, as far as VS is concerned, you're originating your trip at JFK, and you're entirely at their mercy if you miss the flight you're ticketed on for **any** reason