CL60 FLC DEP FROM KIWA FAILED TO COMPLY WITH ATC VECTOR AS CLRED.

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I WAS PNF ON A DEP FROM KIWA. WHILE STILL ON THE GND; THE PF COPIED THE ATC CLRNC; WHICH READ IN PART; 'AFTER DEP TURN R HDG 90 DEG VECTORS FOR....' SHORTLY AFTER THE PF RECEIVED THE CLRNC; I ENTERED THE COCKPIT TO DISCUSS OUR FLT; IT WAS THEN THAT HE BRIEFED ME ON THE RTE OF FLT. THIS OCCURRED APPROX 45 MINS TO AN HR BEFORE DEP. AFTER ENG START AND DURING TAXI; WE COMPLETED CHKLISTS AND CONDUCTED A THOROUGH SAFETY BRIEF ON TKOF AND ABORT PROCS. THIS FLT WAS BEING CONDUCTED AS A CHK FLT WITH FAA INSPECTORS ONBOARD. 1 WAS IN THE JUMPSEAT BTWN THE 2 PLTS. THE TWR CLRED US FOR TKOF WITH NO CLBOUT OR HDG INSTRUCTIONS GIVEN. THE ACFT ACCELERATED AND CLBED VERY QUICKLY. WE WERE HANDED OFF TO DEP CTL IMMEDIATELY; AND WE LEVELED OFF AT THE ASSIGNED ALT OF 3000 FT; ON THE RWY HDG. DURING THE LEVELOFF; BOTH PLTS OBSERVED THE TCASII DISPLAY CONTAINED MANY TARGETS; BUT IT CONVEYED A HEIGHTENED SENSE OF CAUTION. ABOUT 30 SECONDS OR SO AFTER LIFTOFF; THE PF ASKED ME TO 'VERIFY THE TURN' WITH DEP CTL. THE PF KEPT THE AIRSPD BELOW 200 KTS. RADIO TFC WAS HVY; RESULTING IN A SEVERAL SECOND DELAY BEFORE I GOT THE CALL IN. DEP CTL GAVE ME A R TURN; I ACKNOWLEDGED. HE THEN CAME BACK AND ADDED SOME PHRASEOLOGY SIMILAR TO 'MAKE IT A TIGHT TURN.' THE PF COMPLIED. ALL OF THIS OCCURRED WITHIN 35-45 SECONDS AFTER LIFTOFF FROM THE RWY. NO TCASII TA'S OR RA'S OCCURRED. A FEW MINS LATER; THE DEP CTLR CAME ON THE FREQ WITH A PHONE NUMBER TO CALL TO DISCUSS A 'POSSIBLE DEV.' SEVERAL HRS LATER ON THE GND; THE PF TRIED MANY TIMES TO CALL THE NUMBER GIVEN AND RECEIVED ONLY BUSY SIGNALS. SOME PERCEPTIONS AND HUMAN FACTORS: THE LARGE LAG TIME BTWN RECEIPT OF THE ATC CLRNC AND THE ACTUAL DEP WAS POPULATED WITH A GREAT DEAL OF ACTIVITY SURROUNDING THE FAA EVALUATORS ONBOARD THE ACFT. ACFT IS BRAND NEW TO THE CREW AND COMPANY. THE TAXI OUT WAS UNEVENTFUL. THE CLRNC FOR THE R TURN WAS NOT ACCOMPANIED BY ANY ADDITIONAL INFO; SUCH AS; 'WITHIN X MI;' OR 'IMMEDIATE R TURN;' ETC. THIS MIGHT HAVE CONVEYED A SENSE OF URGENCY OR IMPLIED A NEED TO PROTECT SOME OTHER AIRSPACE. AT THE TIME OF TKOF; THE 'R TURN' INSTRUCTION WAS NOW ALMOST AN HR OLD AND HAD NOT BEEN HEARD SINCE. IT WAS ONLY AFTER THE GEAR AND FLAP RETRACTION THAT IT CAME TO MIND; AND EVEN THEN THE PF FELT HE HAD TO VERIFY IT WITH ATC. THIS IS A NEW ACFT FOR US. AUTOTHROTTLES CTL THE TKOF SO ACCELERATION IS RAPID; THE CLB IS RAPID; FLAP AND SLAT RETRACTION OCCURS IN 2 STAGES AT CERTAIN AIRSPDS; AND THE LEVELOFF MUST BE ACCOMPLISHED IN SUCH A WAY TO KEEP THE PAX IN THEIR SEATS. THIS IS A VERY BUSY 30 SECONDS; AND WAS LIKELY THE REASON FOR MY DISTR FROM REMINDING THE PF OF THE CLRNC FOR THE R TURN UNTIL WE WERE LEVELING OFF. THE PROPER TIME TO GET ANY CLARIFICATION ON THE TURN WOULD HAVE BEEN BEFORE WE BEGAN THE TKOF ROLL; BUT THIS WAS DILUTED; IN MY OPINION; BY 3 THINGS: 1) RELIANCE ON CLBOUT INSTRUCTIONS FROM THE TWR THAT WE HEAR EVERY DAY THAT ARE GIVEN IN THE SAME SENTENCE WITH THE TKOF CLRNC. 2) MENTAL AND EMOTIONAL ACTIVITY ASSOCIATED WITH A BRAND NEW ACFT AND PRESENCE OF AN FAA EXAMINER. 3) LONG TIME LAG BTWN THE DELIVERY OF THE CLRNC TO THE TKOF. WE HAVE TO BE ALERT. THE ATC SYS IS FILLED WITH FAMILIAR PHRASES AT PARTICULAR TIMES THAT WE COME TO EXPECT TO THE DEGREE THAT IT BECOMES A CADENCE. WE MAY THINK SOMETHING WAS INCLUDED; WHEN IT WASN'T. THESE WORDS MEAN THINGS.