A character who's number of completions for a particular raid quest is evenly divisible by 20 will recieve the new raid end quest reward. This results in most characters needing fewer than 20 repetitions to get the bonus end reward the first time.
A few characters will need to complete the quest 20 more times if they happen to have just completed their 20th (or 40th or 60th etc) run just before Module 5 goes live. We felt that it was better to give out early raid loot to most characters rather than having special case (i.e. risky) code to reset everyone to 0.