FLC OF AN S80 IS ISSUED TFC AND SIGHTS IT ON THE TCASII. TFC IS BELOW BUT TCASII SHOWS IT MUCH CLOSER THAN ATC STATED. THEY BEGIN A TURN AWAY FROM THE TFC AND GET AN ALERT TO CLB. TFC IS CLOSING AND THEY RESPOND TO THE ALERT.

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ACFT WAS LEVEL AT 6000 FT AND 210 KTS ABOUT TO TURN L BASE FOR RWY 11L AT TUS. APCH CALLED TFC AT 12 O'CLOCK AND 1 MI 1000 FT BELOW. TCASII VERIFIED THE TFC AND SHOWED THE OTHER ACFT 900 FT BELOW US. THE COPLT AND I WERE LOOKING OUTSIDE AND BELOW WHEN WE RECEIVED A TA AND SAW AN ACFT AT THE 12:30 O'CLOCK POS AT THE SAME ALT APPROX 1500 FT AND CLOSING WHILE FLYING AWAY FROM US. I WAS HAND FLYING AND INITIATED A L TURN TO AVOID THE CESSNA AND GLANCED AT THE TCASII WHICH SHOWED THE ACFT 200 FT BELOW US. IT APPEARED THE ACFT I WAS TURNING AWAY FROM WAS AT OUR ALT OR SLIGHTLY ABOVE US. AT THIS INSTANT; I RECEIVED AN RA TO INCREASE CLB TO 2000 FPM. CONTINUED MY TURN AWAY FROM THE ACFT AND TOWARDS THE FIELD WHEN I REALIZED THE TCASII MAY BE RESPONDING TO DIFFERENT ACFT. A GLANCE AT THE TCASII SHOWED THE TARGET ON THE AIRPLANE SYMBOL AND 1000 FT BELOW US. BEGAN ADDING PWR AND CLBING WHILE I CONTINUED MY TURN AWAY FROM THE CESSNA. ABOUT 2 SECONDS LATER; TCASII STATED 'CLR OF CONFLICT' AND WE CONTINUED OUR TURN TO THE FIELD AND STOPPED THE CLB. THE OTHER ACFT CAME NO CLOSER THAN 500 FT AT THE SAME ALT. IN A PHONE CONVERSATION FOLLOWING THIS EVENT WITH TUS APCH; THEY STATED THE CESSNA JUMPED FROM 1000 FT BELOW TO OUR ALT IN ONE SWEEP AND THAT THE CESSNA WAS IN SIGHT. THE INACCURATE ALT CAUSED CONFUSION.