A 4n electron electrocyclic ring opening reaction can be considered to have 2 components – the π-system and the breaking σ-bond.  With respect to the π-system, the reaction is suprafacial.  However, with a conrotatory mechanism, as shown in the figure above, the reaction is antarafacial with respect to the σ-bond.  Conversely with a disrotatory mechanism it is suprafacial with respect to the breaking σ-bond.
By the above rules, for a 4n electron pericyclic reaction of 2 components, there must be one antarafacial component.  Thus the reaction must proceed through a conrotatory mechanism.  This agrees with the result derived in the correlation diagrams above.