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.