Sterling
I would like to help but there is just too much missing information that could have a bearing on what you are seeing.  I have the following questions when I read your post:

1. 10 CLM project created with defaults - what defaults do you mean? what specific process templates or options when you created these projects? where they created using LPA? if so, what process template was applied to CCM, QM and RM project area of each CLM project
2. The user you added - what roles did you assign to the user in the CCM, QM and RM project area context.
3. LPA does provide a way manage the members of a Lifecycle Project. From the members page, you can add or remove members and manage the process roles assigned to a member in each artifact container. See a page similar to this URI to access the members page in your deployment:  https://clm.jkebanking.net:9443/admin/web/members
   

When I was trying to understand what you wanted, I looked at my own sample Money that Matters. When I was logged on as 'clmadmin', the overall admin user I used to create this sample lifecycle project, I noticed the following with the Home button:
a) I could see a list of all projects, but it was not the same as the list of My Projects.
b) for the project, TestProject', that was not listed in My Projects, I visited the project area properties Overview page. I noticed that 'clmadmin' is not a member of 'TestProject', even though it was created by clmadmin. It is only listed as the Administrator.
I then tried to find a user that was a member of only one artifact container, the RM one and the user was curtis. If I logged in as Curtis, and went to My Projects for RM, it only listed one project, the RM project.  If I then removed curtis as a member of that RM project, and went to My projects for RM, no projects were listed.

I would suggest looking at the Overview page of the project area properties of one of the project areas that you did NOT add this new user to and see what the Member listing has to say.