ACR TURBOPROP FLC INITIATE TCASII EVASIVE; EXPEDITED CLB ON VFR DEP FROM SBP WHEN CONFLICTING WITH A PA28 ENTERING THE TFC PATTERN.

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PRIOR TO TAKING THE ACTIVE RWY AT SBP (RWY 29); I WAS AWARE OF ONE ACFT IN THE VICINITY THAT COULD BE A FACTOR DURING OUR DEP. WE HAD WITNESSED A PA28 MAKE A VERY HIGH APCH TO A MISSED APCH/GAR AND HE WAS STILL UPWIND FOR RWY 29 WHEN WE TOOK THE RWY. HE PROCEEDED TO MAKE R TFC AND I KEPT HIM IN SIGHT DURING OUR INITIAL CLBOUT AS HE PASSED OFF OUR R SIDE. AT THAT TIME; THE TWR ISSUED A TFC CALL TO US REGARDING A PA28. I ASSUMED; WITHOUT LISTENING VERY CAREFULLY TO THE XMISSION; THAT HE WAS TALKING ABOUT THE ONE ON THE R. I SAID TO THE CAPT (PNF) 'HE'S IN SIGHT.' THE PNF XMITTED A SIMILAR REPLY TO TWR AND I BEGAN A L TURN TO PROCEED DIRECT RZS VOR; IN A VFR CLB PER OUR CLRNC. THERE ARE NUMEROUS HILLS IN THE VICINITY OF SBP; SO WE TOOK THE OPTION OF A VFR CLB TO AVOID THE MORE TIME CONSUMING IFR ROUTING. I BELIEVE I INITIATED MY L TURN AT ABOUT 600 FT AGL OR SO; AN ALT THAT SEEMS WAY TOO LOW TO ME NOW -- CONSIDERING VFR OPS WERE UNDERWAY. I WAS THINKING IN TERMS OF IFR RULES AT THE TIME (400 FT AGL BEFORE THE FIRST TURN). WHEN WE WERE ALMOST THROUGH A 180 DEG TURN AND CLBING AT 2000 FPM; THE TCASII ISSUED AN RA TO INCREASE CLB; WHICH I RESPONDED TO. AT THIS POINT; THE CAPT SAW THE PA28 FOR THE FIRST TIME -- ABOUT 300-400 FT DIRECTLY BELOW US. I BELIEVE THE NMAC WAS CAUSED BY POOR COM BTWN THE CREW AND ATC; BY A TURN THAT WAS TOO LOW FOR THE OPS AND FLT CONDITIONS; INADEQUATE TFC SCAN; COMPLACENCY IN TREATING A MORE DANGEROUS VFR DEP AS IF IT WERE AN IFR DEP. IN ADDITION; I WAS SUFFERING THE EFFECTS OF A COLD AND FELT TIRED. NO MEDICATION WAS USED.