Inherited authorizations from bucket to item are not synchronized to the Project Management project. Only authorization which are assigned directly on the item itself are synchronized to the project. In SAP-Note 1249825 you can find information, if you want to synchronize inherited authorizations from the item to the project.
A suitable logic of BAdI INM_OF_SYNC with method GET_AUTHORIZATION_SYNC can be used to read the inherited authorization and to pass this to the synchronization framework.
Troubleshooting and Debugging Guide: Decision Flow Management (Tips)