The module security is only available when project security is set to prototype/demo or production.
If Module security doesn't appear when project security is turned on, then something strange has happened.
Ensure that after switching security level you click OK instead of Cancel :-)
I think the issue is that you have not yet 'connected' your module roles to your project roles.
You say you created an Administrator role on the project level, which is correct. However, as the learning module explains, you still have to define what this project role 'Administrator' can do/see per module. Per module you can create roles, after which you can grant this role to a project role, as is depicted on the image in the learning module:
Does this address and solve the issue, or did I misunderstood?