The DPS legendary ring effect is best used to quickly destroy the Siege Weapon spawns. This can be most efficiently achieved by activating the ring while there are many other adds to kill, but while the Siege Weapons are en route or have already reached the raid. If the ring is used at the start of the fight, under Bloodlust/ Heroism/ Time Warp, it will come off CD well after the second wave of Siege Weapons, but also well before the third wave. Players could hold the legendary ring effect for the third wave (the Felfire Artillery) and then use it again on CD to deal with the fifth and seventh waves.
The healer legendary ring can be used to help the raid survive the Felfire Volley spam that occurs after Gorebound Felcasters use Metamorphosis to transform into Gorebound Terrors. This will have the side effect of putting up powerful shields that can help the raid survive the next Gorebound Terror, or other incidental raid damage.
The tank legendary ring can be used to mitigate damage from Gorebound Berserkers when the current tank has high stacks of Slam.