JFK CTLR FAILS TO RECOGNIZE INCORRECT DEP PROC OF IFR ACFT.

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AT XA11Z; I CLRED THE ACFT FOR TKOF ON RWY 31L. DUE TO AIRSPACE CONSTRAINTS (LGA AIRSPACE LIES ABOUT 3 MI TO THE N/NW); DEPS ARE ISSUED AN INITIAL TURN BY CLRNC DELIVERY WHEN THEY RECEIVE THEIR IFR CLRNC. THIS TURN IS ISSUED IN THE FORM OF A PUBLISHED CLB. GENERALLY; THE DEPS TURN L; AWAY FROM THE ADJACENT AIRSPACE. THE ACFT IN QUESTION WAS NOT ISSUED A TURN BY CLRNC DELIVERY; UNBEKNOWNST TO ME. I LOST SIGHT OF THE DEP JUST AFTER LIFT-OFF (DUE TO THE LOW CEILING/VISIBILITY); BUT OBSERVED THE ACFT ON RADAR. ON THIS DEP CONFIGN; BEFORE SWITCHING THE DEP OVER TO DEP CTL FREQ; MOST OF US WATCH TO SEE THAT THE DEP IS IN A TURN AWAY FROM THE ADJACENT AIRSPACE. I AM IN THE HABIT OF DOING THE SAME THING. UNFORTUNATELY; SINCE I COULD NOT OBSERVE THE ACFT VISUALLY; I WAITED ON RADAR TO OBSERVE THE TURN. WHEN IT APPEARED THE ACFT WAS NOT TURNING; I LOOKED AT THE FLT PROGRESS STRIP; WHICH HAD NO DEP CLB WRITTEN ON IT (THE CLB ISSUED IS NORMALLY WRITTEN ON THE FLT PROGRESS STRIP). HOWEVER; IN MY MIND; I BEGAN QUESTIONING WHETHER THE ACFT REALLY DID HAVE THE TURN ISSUED BY CLRNC DELIVERY; AND CONTINUED TO WAIT TO SEE IF THE ACFT WOULD TURN. WHEN THE DEP WAS STILL NOT TURNING; I ISSUED A HDG FOR THE ACFT TO TURN AWAY FROM THE AIRSPACE. UNFORTUNATELY; I HAD WAITED TOO LONG; AND THE ACFT CAME WITHIN LESS THAN 1 1/2 MI FROM THE AIRSPACE BOUNDARY (1 1/2 MI IS NORMALLY THE MINIMUM REQUIREMENT). I ISSUED ANOTHER TURN; FURTHER AWAY FROM THE AIRSPACE; AND THE ACFT EVENTUALLY BECAME PROPERLY SEPARATED FROM THE ADJACENT AIRSPACE. I COULD HAVE AVOIDED THIS SIT IF I HAD OBSERVED THE LACK OF STRIPMARKING (INDICATING A TURN HAD BEEN ISSUED) ON THE FLT PROGRESS STRIP; AND BY ISSUING A TURN EARLIER. I CANNOT ASSUME A TURN WAS ISSUED; WHEN THE STRIP SHOWS NO TURN ISSUED. ALSO; I POINTED OUT THE ERROR TO THE CLRNC DELIVERY PERSON; WHO DIDN'T REALIZE THE GRAVITY OF THE SIT -- THAT EVERY DEP NEEDS TO BE ISSUED A TURN (THE CLRNC DELIVERY PERSON HAS ONLY BEEN ON THE 'FLOOR' FOR A MONTH OR SO). IN THE FUTURE; I WILL NOT HESITATE TO ISSUE AN IMMEDIATE TURN; WHEN I OBSERVE STRIPMARKING THAT IS NOT COMPLETE OR CORRECT.