How users access public folders and what to do when they cannot access them?

Hello whart1336, 
Answering your questions, 

When is this value "EffectivePublicFolderMailbox" set on the user ? 
The EffectivePublicFolderMailbox is stamped on the mailbox once the mailbox created, the system will start to assign a fully synchronized public folder mailbox that is not excluded from serving hierarchy

When does it get calculated ? 
The EffectivePublicFolderMailbox is calculated if,

1.New mailbox requires a new public folder mailbox assignment

2.Admin chose to leverage system(EffectivePublicFolderMailbox) public folder mailbox assignment instead of manual assignment using DefaultPublicFolderMailbox parameter
3.One of the hierarchy assigned public folder mailboxes is excluded from serving hierarchy

Let me know if you have other questions/concerns.