NMAC BTWN A PIPER PA28-140 AND A TWIN CESSNA CONVERGING IN THE TMB TFC PATTERN AT 1000 FT. TWR CTLR HAD ISSUED TA.

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WHILE WE WERE PARALLEL TO THE THRESHOLD OF RWY 9L WE RECEIVED A TA AT 11 O'CLOCK LNDG RWY 9L AS #1 AND WE SHOULD FOLLOW THAT ACFT. I ASKED THE CFI TWICE ABOUT THE TFC DUE TO OUR R BECAUSE I FELT THIS TO BE MORE A THREAT THAN THE OTHER LNDG TFC (AT THIS POINT IN TIME). INSTEAD OF WATCHING OUT FOR THE TFC; I REALIZED THAT HE STARTED AGAIN TO SET UP THE GPS/AUTOPLT FOR A DSCNT TO 500 FT; AND HAD HIS HANDS ON THE CTL YOKE; ATTEMPTING TO ENGAGE THE AUTOPLT (NOT SURE ABOUT IT -- MAYBE?). SECONDS LATER I SAW THE TWIN ENG PROP AT OUR 2 O'CLOCK POS FILLING THE R WINDOW AND CLOSING IN. THE HORIZ DISTANCE WAS; MAX; AROUND 300 FT. I SHOUTED 'MY CTLS; KEEP YOUR HANDS OFF' AND SIMULTANEOUSLY PUSHED THE YOKE DOWN AND LEFT DSNDING FAST AND EXCEEDING VNO; LEVELING OFF AT 500 FT THEN TURNING BACK TO A 270 DEG HDG. THE TWIN ACFT PROBABLY DIDN'T SEE US; AS WE WERE SLIGHTLY BELOW HIS GLIDE PATH AT ALL TIMES. HE OBVIOUSLY WAS IN A RUSH TO GET IN TO THE ARPT; MAYBE FOLLOWED BY A LATE HDOF FROM MIA APCH (MIA CLASS B AIRSPACE IN CLOSE VICINITY AND HE WAS PROBABLY ONLY LATE DSNDING AFTER TRANSITIONING THROUGH THE APCH PATH OF MIA). I WAS NOT SURE IF THE CFI HAD ENGAGED THE AUTOPLT AGAIN (NO CLR WARNING LIGHT IN THE VISUAL RANGE IN FRONT OF THE PLT; JUST LCD; HARD TO READ WITH SUN OR LIGHT REFLECTION IN THE COCKPIT) OR IF I JUST WAS 'OVERRIDING' THE CFI'S CTL MANUAL INPUTS ON THE YOKE (HE STILL HAD HIS HAND TIGHT ON IT) TRYING TO CONTINUE TO FLY STRAIGHT AND LEVEL. DUE TO THE STRONG XWIND WE WERE PUSHED RIGHT INTO THE APCH PATH FOR RWY 9L; SO I TURNED FURTHER R. THERE WAS SUBSTANTIAL CONFUSION WITH THE TWR ON THE RADIO FOLLOWING THIS EVENT. I SAW THE OTHER ACFT FOR RWY 9L ABOUT 3 MI AWAY. ATC ADVISED US TO TURN TO THE S AND WE WOULD BE #2 TO LAND. BUT THERE WAS NO OTHER ACFT IN BTWN US AND THE RWY 9L SO THE CFI RADIOED THAT WE ARE NOW #1 FOR FULL STOP. TWR ADVISED US TO CONTINUE DOWNWIND WHILE WE HAD ALREADY TURNED FINAL. WE THEN RECEIVED A LNDG CLRNC AND LANDED. WHEN WE HAD LEFT THE RWY WE HEARD ON THE RADIO THAT THE OTHER TFC BEHIND US WAS PERFORMING A GAR.