OK, this is working.
I had invited someone to this tree. They received the invite and accepted. I controlled who they had access to.
This person Added the parents, mother and father, and some details. They added me to the Trust list for the Father and not the Mother. I can see details of the Father, but no details for the Mother. I used the Wiki-Tree email to ask permission to view the mother, that was accepted and I could see the details.
I looked at my Watchlist, saw the two new additions, BUT, noticed that these two were listed as Open. NOT what I wanted. So, requested the profile manager, for these two people, to click on the Privacy setting for the, and change the Setting to the Red ICON (Private). Refreshed the Watchlist, and they are now Private.
I asked this person to look at my profile, and was able to see that I have two children. They saw that I had two children, but would NOT see any details on them.
Lesson Learned: Suggest to the Trusted List participants, that they go immediately to the Privacy Tab, to verify that the Settings are correct. In my specific case, they should be Private ( the Red ICON)