What you configured is the Personas hub (main system - connected systems) scenario.
You have to decide whether you want one central Personas system from which others are accessed or a separate Personas installation in each system. The latter is the recommended approach.
In any case, what seems to be missing is the correct user assignment to systems and/or Personas roles. Each user must be assigned to the system it should be accessing via Personas and also must have a corresponding Personas role assigned in the Personas administration transaction.