In D'zeron , there are leaders who have trained dreaming skills who are given Authority by the Ancients to secretly mediate between the Ancients and the people living on the surface, including both those of D'zeron and those of Jai-Ten . The position of Dream Keeper and the leader of the village of D'zeron are always help by the same person or people, a but a distinction is made still between the role of Dream Keeper and the role of Matriarch or Patriarch . theoretically a non-dreamer married to a Dream Keeper could serve as Matriarch or Patriarch, but this would rarely happen. there may have been a few non-dreaming Patriarchs, though.
To become a fully functioning Dream Keeper one must have the skill of Dream Travel, which is the ability to use the dream plane to transport oneself physically. Dream Keepers require this skill because it is the only way in or out of the undersea world of the Ancients. Thus anyone who manifests this skill in D'zeron is immediately called as a Dream Keeper if they are felt to be trustworthy. Thus Jason and Serai are initiated as dream keepers the night after they are married in the dream plane during which she transports herself into the sealed Temple to consummate their marriage. Jason may eventually learn to do it alone, but he rarely does, usually Serai transports them. Not all dreamers who can Dream Travel have the power to transport another person, this is a very rare skill and requires a very absolute bond with the other person. And the other person needs to have the biological potential for the skill at least.
Tersh and his wife had the skill, probably especially his wife, but they were not trust worthy, because they would reveal information to the people of D'zeron which the Ancients did not want everyone to know. This is why they were not called as dream keepers and why she was so resentful at not being called. and why she became Dream Bound. the Ancients took her from D'zeron. Tersh could not find her because he had not developed the dream traveling skill on his own, being too fragmented in his mind to focus his skills. She was skilled enough to transport him with her, and they had visited the world of the Ancients together. This also would be a good subject for a book.
I'm not sure how they kept her from visiting Tersh and Chathalen , or if Chathalen could visit his mother once he became a dream keeper. I think Chathalen would have been trusted not to tell, because Chathalen was extremely honest about keeping secrets, most of the time. Being able to visit her but not being able to share this with his father would have been very painful for him, adding to his overall state of emotional distress during the time he is taking care of Jason . quite probably he would have confided in Harris eventually, having permission to share with Harris things which cannot be shared with the village. This would contribute to the very close brotherhood between these two men.