How does servant leadership trickle down to impact subordinates' work and non-work outcomes? This study sets out to investigate the mechanisms and boundary conditions associated with this question. In so doing, we integrate two sequential mechanisms (family-supportive supervisor behaviours and work engagement/self-care) and a contextual condition (servant leader's perceived organizational support) to address whether and how servant leaders shape subordinates' work performance and their satisfaction with work-family balance. Using matched supervisor-subordinate data (770 supervisors and 819 subordinates) collected from a group of companies in Chile, our results from multilevel analyses largely support our hypotheses. We contribute to servant leadership and research on family supportiveness by: 1) introducing and discussing two separate and sequential mediating mechanisms to explain the trickle-down effect of servant leadership; 2) emphasizing the role of perceived organizational support in establishing when the trickle-down effect occurs; 3) highlighting the need to bridge two separate bodies of research (namely those of servant leadership and family supportive supervisor behaviours) in developing interventions in organizations to help employees manage work-family issues.