team member as project manager of a sub project

This looks like an issue.
We'll investigate on subject.

Ticket #2501 recorded

After analysis, we could not reproduce this issue.

If I summarize use case, that we reproduced on Demo (you can access it connection as manager/manager) :
=> Connect as manager.
=> Create Project P#2501.
=> Allocate resource Member to P#2501 as Project Member.
=> Create Project P#2501-1 as sub-project of P#2501.
=> Do not allocate resource Member to P#2501-1 (so he should inherit Project Member access from parent)
=> Create Project P#2501-2 as sub-project of P#2501.
=> Allocate resource Member to P#2501-2 as Project Leader.
=> Connect as member.
=> Member has read only access to P#2501 and P#2501-1 and has write access to P#2501-2.
(Project Leader has Acces Mode "Manager" on Project, and Project Member has Access Mode "Reader" on Project)

To be sure, we also changed acces mode for Project Member profile :
=> connect as admin (well we did it but you won't be able to do this on Demo)
=> Set Access Mode as "No access" for Project Member on Project.
=> connect as Member
=> Member has no access to P#2501 and P#2501-1 (does not even see them in project list) and has write access to P#2501-2.

All seems correct for us.
So maybe you changed some access mode or else that leads to different behavior...
Or possible Team Member did not disconnect / reconnect after admin changed rights ....
.... Yes, users do not automatically retreive acces rights changes. For performance reason access rights are stored on connection to avoid dynamic recalculation whenever needed (which is very ofter, and calculate is very complex).

If you still reproduce, please try and reproduce on demo, as we did.
Thanks.

OK, I understand better now.
Visibility is correct, it seems you can update the project, but when you save you're blocked.
Thanks.