Abstract: By using S-act theory and ordered semigroup theory, Condition (PWP_E) in the category of S-posets is introduced, and pomonoids over which cyclic (Rees factor) S-posets satisfy this new condition are characterized. Moreover, a classification of pomonoids is given for which Rees factor S-posets satisfying Condition (PWPE) have some other flatness properties and vice versa. As applications, some important results on Condition (PWPE) are extended.