ACR X NON ADHERENCE TO ATC CLRNC MADE UNCOORD AIRSPACE PENETRATION. PLTDEV.

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I WAS WORKING LCL CTL POS AS AN ATC SPECIALIST AT JFK TWR. AS IS THE NORM AT JFK TWR I ASSIGNED ACR X A PRECOORD HDG OF 100 AND 5000 FT. I CLRED ACR X FOR TKOF FROM INTXN ZA ON RWY 31R AND INSTRUCTED ACR X TO MAKE HIS TURN INSIDE THE ARPT BOUNDARY. AFTER AGREEING TO COMPLY WITH THE INSTRUCTION; ACR X PROCEEDED WITH THE CLBOUT ON A HDG OTHER THAN INSTRUCTED. THIS HDG IF CONTINUED WOULD VIOLATE THE LGA TWR'S AIRSPACE. IT IS THE NORMAL PRACTICE TO POINT OUT SUCH TFC TO LGA TWR. I ATTEMPTED TO DO THIS TO NO AVAIL. I REPEATED TURNING INSTRUCTIONS TO ACR X WITH NO ACKNOWLEDGEMENT. AGAIN I REPEATED THE INSTRUCTIONS; ACR X ACKNOWLEDGED AND COMPLIED. I STOPPED ACR X CLBOUT AT 3000. WHEN CONTACT WITH LGA TWR HAD BEEN ACCOMPLISHED AND ANY POSSIBLE CONFLICTS WERE AVOIDED; I INSTRUCTED ACR X TO CONTACT N90 DEP CTL. SINCE THEN I HAVE BEEN CHARGED WITH A SYSTEMS DEV; HAVING ALLOWED ACR X TO VIOLATE LGA SECTORS' AIRSPACE WITHOUT PRIOR COORD. AT JFK TWR WE DO NOT HAVE DIRECT COM WITH LGA SECTOR AT N90 OTHER THAN TELEPHONE.