ALT ALERTER ALERTS A320 FLC OF ALT OVERSHOOT WHEN FLYING SEA CHINS ARR.

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WE WERE DSNDING INTO SEA ON THE CHINS 2 ARR. WHEN AND AFTER MUCH VECTORING FOR TFC DELAYS; WE WERE DSNDED TO A LOWERED ALT. THERE WAS CONTINUOUS LIGHT TURB DURING THE DSCNT PHASE. THE AUTOFLT SYS WAS ENGAGED USING AUTOTHRUST AND AUTOPLT MODES IN MANAGED DSCNT CONFIGN. THE ACFT SLOWED AND DEPARTED FROM THE MANAGED SPD TARGET RESPONDING TO THE NORMAL LAW; 1 'G' REQUIREMENT BUT WHEN THE TURB SUBSIDED; THE ACFT INCREASED SPD AND INCREASED VERT DSCNT RATE. THE AUTOLIGHT ATTEMPTED TO ENGAGE 'ALT' BUT DID NOT RESPOND SOON ENOUGH TO PERFORM A LEVELOFF WITHIN THE ALLOTTED AIRSPACE. THE ACFT DSNDED ABOUT 300 FT BELOW ASSIGNED ALT. THE ALT WARNING HORN SOUNDED AND I IMMEDIATELY PULLED VERT SPD. THIS LEVELED THE AIRPLANE AND STARTED A SLOW CLB BACK TO THE ASSIGNED ALT. THERE WAS NO TFC CONFLICT. MOST OF THE A319'S AND A320'S IN OUR FLEET WILL COMMAND AND PERFORM LEVELOFF MANEUVERS WELL IN ADVANCE OF THE ACTUAL SELECTED ALT. I WAS EXPECTING THIS TO OCCUR IN THIS INSTANCE BUT WITH THE TURB AND THE HIGH RATE OF DSCNT (4500 FPM) THIS PARTICULAR AIRPLANE DID NOT PERFORM CONSISTENT WITH PREVIOUS EXPERIENCE. MY ATTN WAS DISTR MOMENTARILY BY DSCNT PLANNING AND ATC INSTRUCTION ABOUT THE TIME WE REACHED LEVELOFF. I'M SURE THAT HAD MY FULL ATTN BEEN GIVEN TO THE DSCNT PERFORMANCE; I WOULD HAVE CAUGHT THE ERROR IN TIME TO PREVENT THE ALT EXCURSION IN THIS EVENT.