I've completed my own quest to become Knight Enchanter and learned that specialization. Some of my companions have their specialization available in the skill tree as well, e.g. Necromancy for Dorian or Reaver for Iron Bull.
But most of my companions don't have their specializations unlocked, Blackwall and Cassandra for example still only have the original four ability types available they had from the start. All my companions are level 10, so that is not the reason.
What exactly unlocks the specializations for companions, and why aren't they unlocked for all of them in my case?