Narrative:

The G4 was descending from 12000 ft and the VFR traffic at 11700 ft (aircraft #2) was 12 O'clock and 5 mi. I quoted traffic. When they were 2 mi apart, pilot of G4 advised he had an RA. I asked was he climbing or descending since I had observed his mode C at 11500 ft and the traffic showed 11700 ft. He advised he was climbing. There was also an E135 departing sjc leaving 11500 ft. The G4 climbed to 13000 ft and caused a conflict with the E135 which I turned 40 degrees right and expedited. This situation was abnormal because I would have expected the G4 to descend, not climb, for the VFR traffic. If he had descended there would have been no problem with the E135.

Related reports:

Google
 

Original NASA ASRS Text

Title: ZOA CTLR ISSUED VFR TFC TO DSNDING G4 FOR SJC, G4 RESPONDED TO TCASII RA AND THEN CONFLICTED WITH THIRD ACFT DEPARTING SJC.

Narrative: THE G4 WAS DSNDING FROM 12000 FT AND THE VFR TFC AT 11700 FT (ACFT #2) WAS 12 O'CLOCK AND 5 MI. I QUOTED TFC. WHEN THEY WERE 2 MI APART, PLT OF G4 ADVISED HE HAD AN RA. I ASKED WAS HE CLBING OR DSNDING SINCE I HAD OBSERVED HIS MODE C AT 11500 FT AND THE TFC SHOWED 11700 FT. HE ADVISED HE WAS CLBING. THERE WAS ALSO AN E135 DEPARTING SJC LEAVING 11500 FT. THE G4 CLBED TO 13000 FT AND CAUSED A CONFLICT WITH THE E135 WHICH I TURNED 40 DEGS R AND EXPEDITED. THIS SIT WAS ABNORMAL BECAUSE I WOULD HAVE EXPECTED THE G4 TO DSND, NOT CLB, FOR THE VFR TFC. IF HE HAD DSNDED THERE WOULD HAVE BEEN NO PROB WITH THE E135.

Data retrieved from NASA's ASRS site as of July 2007 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.