ACR BE02 FLC AWARE OF CLBING BE90 TFC; BUT NO VISUAL CONTACT. BE90 HAS BE02 IN SIGHT AND COMMENCES VFR CLB. BE02 TCASII RA CLB MANEUVER INITIATED WHEN BE90 IS ALREADY ABOVE THE BE02. BE02 CLBS THROUGH BE90 ALT; AND RECEIVES A TCASII RA DSCNT COMMAND; BUT IS ARRESTED BY PIC. ATC TRIED TO STOP CLB ACTION; BUT BE02 PIC ADVISES THEY WILL FOLLOW RA COMMAND.

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FROM OUR POS LISTED ABOVE; WE NOTICED; BUT WERE UNABLE TO VISUALLY ACQUIRE; AN ACFT ON OUR TCASII SCOPE AT 2 O'CLOCK POS AND 10 MI. THIS ACFT WAS IN A SLOW CLB FROM 300 FT BELOW OUR ALT. APCH CALLED THIS ACFT AND GAVE HIM TFC 'A BEECHCRAFT 1900 AT 10 O'CLOCK POS AND 10 MI AT 11000 FT.' THE ACFT SAID HE HAD US IN SIGHT AND WAS TOLD TO MAINTAIN VISUAL SEPARATION WITH US. APCH THEN CALLED US WITH TFC. HOWEVER; JUST AS HE SPOKE WE RECEIVED A TCASII RA 2500 FPM CLB; WHICH WE OBEYED BECAUSE THE TFC WAS NOT IN SIGHT. THE TFC WAS ALREADY 200 FT ABOVE US SO THIS RA TOOK US THROUGH THEIR ALT. APCH WANTED US TO DSND TO 7000 FT; BUT WE TOLD HIM WE WERE IN A TCASII CLB. NOW; SAFELY ABOVE THE TFC; THE TCASII COMMANDED A 2500 FPM DSCNT. WE IGNORED THIS RA BECAUSE WE SAW THE ACFT PASS BENEATH US. THIS SECOND RA ALSO WANTED US TO PASS THROUGH THE ALT OF THE TFC. WHEN WE FIRST TOLD THE CTLR WE WERE IN A TCASII CLB; HE ASKED WHY WE HAD TO CLB IF THE OTHER ACFT HAD US IN SIGHT. I EXPLAINED THAT WE DIDN'T HAVE HIM IN SIGHT. I BELIEVE THE CTLR'S CONFUSION ABOUT WHEN WE MUST ACT ON AN RA; CONTRIBUTED TO ALLOWING THE OTHER ACFT CLOSE ENOUGH TO CAUSE AN RA. I ALSO BELIEVE THE OTHER ACFT; NOT HAVING TCASII; DOESN'T UNDERSTAND HOW MUCH ROOM TO GIVE A TCASII EQUIPPED ACFT SO AS NOT TO GIVE THEM AN RA. POINTING OUT TFC TO IFR ACFT BEFORE VFR ACFT MAY ALSO HELP TO AVOID THIS SIT. SUPPLEMENTAL INFO FROM ACN 408048: APCH NEVER CALLED OUT VFR KING AIR TFC OUT TO US. I; AS COPLT (PF) IMMEDIATELY RESPONDED TO TCASII YELLOW INTRUDER TFC; TFC COMMAND. THE CAPT ASKED IF I SAW TFC. I RESPONDED YES; SAW ACFT PASS BELOW OUR R OUTBOARD WINGTIP APPROX 100 FT BELOW AND 25 FT HORIZLY DIAGONALLY TOWARDS OUR 8 O'CLOCK REAR POS.