Air carrier pilot reported receiving a TCAS RA while on base leg to PIE which required evasive action to avoid a VFR aircraft not in contact with ATC maneuvering in their path. Reporter expressed concern with ATC operational procedures at PIE.

Narrative

On our arrival into PIE; we received an RA on our extended base leg for runway 36. The RA was a reversal; we were initially instructed to climb and then shortly after descend with a clear of conflict notice maybe 5 seconds later. We were not issued a traffic call from ATC. I noticed when the controller gave us the base leg heading that there was traffic about 5 nm ahead of us that was cutting in and out on the ND. It initially appeared as an aircraft climbing rapidly and disappeared from our screen due to being out of conflict range. When we were closer they appeared on our screen again; I told the Captain we needed a left turn immediately or we will get an RA as it looked like they weren't moving left or right. My initial thought was a helicopter. I saw the plane; they were doing spins over the coast and in a spin at 12 o'clock as ATC approved the left turn to avoid them. We received the first climb instruction when we were in the left turn and I responded accordingly. When the pilot monitoring told ATC 'responding to an RA'; the controller responded with 'Well he wasn't there when I issued the turn'. It also seemed that the controller was dealing with a possible emergency as there was a twin aircraft on frequency who couldn't get their second engine started. Because of this it seemed the controller slowed us down to 190 kts farther out than normal. In my opinion this was a close call due to the fact that the airplane was doing aerobatic maneuvers. If the turn wasn't issued I'm not sure the RA would have successfully avoided a collision.I believe there needs to be a notice sent to Albert Witted airfield that airplanes doing maneuvers over the coast in the arrival area of PIE and SRQ need to be talking to approach control for flight following. This could have easily been avoided if they were on frequency. ATC also needs to keep commercial aircraft going into PIE in controlled airspace at all times below 6;000 feet. The current arrival procedures into PIE specifically Runway 36 are a recipe for a disaster.