There was an update on this earlier today:
It looks like the game needs to “know” that your alt is eligible for Essences of Ny’alotha by you having already logged in to a character that has a rank 3 essence your alt doesn’t have. Similar to how the mount achievements require you to log in to the character that has the most mounts to push the count, the game can’t “see” all your other characters when you log in to one.
Of course this isn’t going to help anybody that has already had the problem and nobody will read this except people who had the problem looking for a solution 
But at least you will know for next time.