A C560 FO CHANGED L FLT DIRECTOR MODES CAUSING AN INCORRECTLY SET R FLT DIRECTOR PANEL TO INITIATE AN UNCOORD DSCNT.

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ON OCT/SUN/05 MY FO AND I WERE FERRYING A CITATION 560 ULTRA FROM LIT TO LUK. AT AN ALT OF FL290; ABOUT 60 MI SW OF ABB VORTAC; I WAS IN THE R SEAT AND AS A COURTESY I ALLOWED THE FO TO FLY FROM THE L SEAT SINCE HE IS UPGRADING TO PIC STATUS WITH THE COMPANY. WE WERE RAPIDLY APCHING LUK. I HAD ALREADY OBTAINED ATIS AT LUK AND I WAS IN THE PROCESS OF 'SETTING UP THE APCH;' WHICH WAS A LOC BACK COURSE TO RWY 3R. FOR SOME REASON; MY FO WAS 'EXPERIMENTING' WITH THE MFD. I WAS NOT SURE WHAT HE WAS DOING; BUT I WAS NOT CONCERNED AND I CARRIED ON WITH WHAT I WAS DOING. WHAT I SOON DISCOVERED WAS THAT THE FO SWITCHED THE SYMBOL GENERATOR ON THE MFD. WHAT THIS CAUSED TO HAPPEN WAS THAT THE AUTOPLT AUTOMATICALLY SWITCHED TO 'MY SIDE.' THIS ACFT HAS THE PRIMUS 1000 (HONEYWELL) AVIONICS SYS. IT HAS 2 FLT DIRECTOR MODE SELECTOR PANELS. THE AUTOPLT WAS BEING CTLED BY THE FO'S MODE PANEL WHICH WAS CORRECTLY SET WITH ALT HOLD AND LNAV. WHEN HE SWITCHED THE SYMBOL GENERATOR; THE AUTOPLT SWITCHED TO MY SIDE. MY MCP WAS NOT SET TO ALT HOLD. THE ACFT GRADUALLY DSNDED TO FL286. THE ALT ALERTER WAS SET CORRECTLY. I DID NOT HEAR THE 'CHIME' THAT ALERTS THE PLTS TO AN ALTDEV. I AM SURE IT CHIMED AND I DID NOT NOTICE IT SINCE I WAS CONCENTRATING ON STUDYING THE APCH PLATE AND SETTING THE APCH. ANYWAY; THE CTR CTLR HAD US SAY OUR ASSIGNED ALT AND THEN HAD US CHK ALT. WE IMMEDIATELY CORRECTED. ATC DID NOT ADVISE US OF ANY TFC CONFLICTS NOR DID THEY HAVE US 'CALL' THE CTR. WE CONTINUED TO LUK WITHOUT FURTHER INCIDENT. I FEEL THAT THIS INCIDENT HAS 2 FACTORS: FIRST; THE FO'S LACK OF KNOWLEDGE WITH THE AVIONICS SYS. I DID NOTICE THE MFD 'FLICKER' WHEN HE SWITCHED THE SYMBOL GENERATOR; I KNEW THAT A CHANGE OF THE SYMBOL GENERATOR WOULD RESULT IN HAVING TO RESET THE AUTOPLT AND MCP. HOWEVER; I FELT THAT THE FO WOULD KNOW THIS. SO THE SECOND FACTOR IS MY LACK OF OVERSIGHT OF THE FO AND MY MISGUIDED TRUST IN HIS ABILITIES. I WORK FOR A LARGE FRACTIONAL AND EVERY TOUR I HAVE A DIFFERENT FO. ALL THESE GUYS COME IN VARIOUS LEVELS OF EXPERTISE AND ABILITY AND I MUST QUICKLY EVALUATE THESE GUYS AND THEIR ABILITY. IF I DEEM A PLT TO BE WEAK; THEN I WILL 'BABYSIT' THEM. I MISJUDGED THIS GUY'S ABILITIES AND OBVIOUSLY DID NOT PROVIDE SUFFICIENT OVERSIGHT. AS PIC; I ASSUME ALL RESPONSIBILITY. I WOULD NOTE THAT AS A FAIRLY NEW PIC; IT IS SOMETIMES VERY DIFFICULT TO SUPERVISE A WEAK PLT AND STILL FULFILL ALL OF MY DUTIES IN THE EXTREMELY CHALLENGING FRACTIONAL FLYING WORLD. THE COMPANY NEEDS TO BETTER TRAIN AND ENSURE THAT ALL FO'S ARE COMPETENT. THERE ARE TOO MANY WEAK FO'S I MUST DEAL WITH.