A phased project has a different manager for each phase. All the managers have Manager Level Access in security, but none of them can find the phase they manage in the projects list.
This is the expected behavior in Core. The Manager Level Access security profile only gives you access to the projects you manage. For phased projects, you must be the manager for the parent project before you can see the phases under it. As a workaround, you can search for the phase you manage from the screen level search in the Projects screen. The phase shows up in the search results and you can view its details. Another option would be to have your Core administrator customize your security permissions and give you access to the projects of other managers. Check out this article for details: Managers see projects managed by them.