Blizzard clarified the final Patch 10.1 chapter will open up to everyone when Scalecommander Sarkareth becomes available in Raid Finder.
The story is tied to the end of Aberrus, so they’ve made two possible requirements for the quest. You can either get it this week if you killed Sarkareth or when the last Raid Finder wing opens during the week of June 19.
(Source)
Just want to be very clear–
The final chapter for the Embers of Neltharion questline will open up to all players, regardless of their personal raid progression, when Scalecommander Sarkareth becomes available in Raid Finder.
That story is related to the end of the raid. So in order for players to see the content as intended, we’ve made two possible requirements for the quest to be given: either (this week) you must have killed Sarkareth, or, for those who do not raid, the last chapter will open to you the same week as the final Raid Finder wing opens.
This way, we’re able to deliver the content to all without spoiling it for players who want to experience it chronologically.
