process starts immediately when trigger is fired. The problem here might be how activities are logged. In Kentico 8 activities are logged into file at first and then they're transformed into database every minute. This could cause the delay.
I suggest you to upgrade to Kentico 8.1 where processing of activities has changed. Now activities are logged to memory and then transformed to the DB every 10 seconds. You can read more about activity tracking in our documentation. There's also information on how to change the interval of activity logging.