This is probably not what happened in this case, but one reason an a/c can be in a rush to push is that there is a ATC delay program in effect at the destination airport and if they miss their slot, they may not be going or will take a huge (hours) penalty. Was there by chance weather issues in TPA causing a delay program there?

I was booked on a flight to ORD from OAK where the flight originally had a delay of 5 hours due to ORD weather and a great decrease in the amount of planes they could land. All passengers had basically been notified of the 5-hour delay. A slot became available and now we were pushed up and left with only a one-hour delay. Those who wandered off due to the expected 5-hour delay did not make the flight. Those of us who stuck around got rushed onto the plane and out of there. Had we have missed that slot though, we would have been back to the old delayed time.

Like I said, that probably doesn't explain what happened to you, but I wanted to explain when/why ATC can cause a rush to get a plane off.