Which email address should the printed Case Report present for the Case Manager in the Role Section of the Report?
This sounds like a bug. If you look in CRM/Case/BAO/Case.php in getCaseRoles() it has this in the SQL:

LEFT JOIN  civicrm_email ON (civicrm_email.contact_id = civicrm_contact.id )

If you change it to

LEFT JOIN  civicrm_email ON (civicrm_email.contact_id = civicrm_contact.id AND civicrm_email.is_primary = 1)

does that fix it?