This is what's known in the ATC world as "wearing all the hats". Usually FLL will only do this after 10pm local and at around 6am ground control will open up and wear the ground and clearance "hats" until around 7am. After this point, it's buisness as usual. It is pretty common. Center controllers will do the same thing. They will wear two or more "sectors". It's not uncommon to hear a center controller say "switch to MY frequency 123.4". What this means is that you are transitioning into the next sector but the you will still be talking to the same guy. It also means that a full initial call on the NEW frequency is NOT required.

Yes, from the "first person" ....  I used to fly for National Jets but I just moved (check your messages). If YOU spot at FLL you will see 22NJ/33NJ/66NJ/77NJ/88NJ/99NJ, usually using a Lifeguard callsign.