It looks like it's working properly from what I can see. I remember now why you won't be able to add members manually to the user group, because it's linked to the external one it'll get refreshed after saving it.
It does look like it's found the group successfully:
2015-11-27 09:17:12 [ldap] [D] op search (7.1ms) [ filter=, base= ]
2015-11-27 09:17:12 [ldap] [D] op search (11.0ms) [ filter=(cn=grp_its_unix_adm), base=ou=groups,ou=unallocated,ou=MYCOMPANY,dc=MYCOMPANY,dc=edu,dc=au ]
2015-11-27 09:17:12 [ldap] [D] op search (147.4ms) [ filter=(cn=grp_its_unix_adm), base=ou=groups,ou=unallocated,ou=MYCOMPANY,dc=MYCOMPANY,dc=edu,dc=au ]
2015-11-27 09:17:12 [ldap] [D] op search (8.7ms) [ filter=(|(|(objectClass=posixGroup)(objectClass=organizationalunit))(objectClass=groupOfUniqueNames)), base=CN=grp_its_unix_adm,OU=Groups,OU=Unallocated,OU=MYCOMPANY,DC=MYCOMPANY,DC=edu,DC=au ]
2015-11-27 09:17:12 [ldap] [D] user_list (175.2ms) [ group=grp_its_unix_adm ]
It will iterate over member, ismemberof, memberof, memberuid and uniquemember attributes of the group so do check from an ldapsearch that it has some of those?
Also check that the login names in Foreman match the member names in LDAP. If it has those attributes, enabling the "sql" logger might also shed some further light as we ought to see queries in the users table.