Hi Adrian,
you do not need to stop the server.
killall -9 php-fpm does what the order suggest. It kills all running php-fpm processes.
Supervise (svc) watch these processes. If they are not running it will start them again.
The killlall thing is only needed when supervice starts new processes when the old are in zombie mode. Which means that they are running and blocking but does not work any longer. So supervise tries to start them again.
To stop and start a service you can use:
svc -d /service/(name_of_service) -d means down
svc -u /service/(name_of_service) -u means up
The list of the running services you can get with
ls -la /service
A simple killall -9 should resolve your problem
The name of the php service is /service/php5-fpm
The name of the running instances is php-fpm
;)