1: Will this special reward be time-locked? Your post seemed to imply that we would have to defeat IZAX prior to 5.9 to receive this prize. I was thinking something like the Dread Fortress and Dread Palace special titles that were rewarded during their "Nightmare Power" events in 2014.
2: Will this special prize be offered for both Story Mode and Master Mode?
1: Yes, it will be time locked between 5.8 and 5.9. You must defeat Izax on Veteran Mode (we are messaging it as Master due to difficulty) during that time to earn the reward. This is very similar to the Nightmare Power event.
2: Veteran (Master) mode only.
3: Quick explanation on the rewards. Beating Izax during this period will grant you a time locked Achievement, exclusive title, and special reward within your legacy. After 5.9 you can no longer earn that Achievement or Title. The special reward will then become a very rare drop off of Izax which will be a BoP version, instead of Legacy-wide.