The global economic recession is relevant in public administration, especially in terms of the human factor. If we pretend to empower people as a resource, a key aspect is the perception of equity in their relationships. Previous research has shown how a positive shared interpersonal justice climate (IJC) in a work team impacts employee well-being, affecting the level of engagement and burnout. This influence is crucial in achieving positive results in the organization and for employees. The objective was to analyze the relationship between IJC and extra-role performance (ERP) and the mediating role of two indicators of well-being (burnout and engagement) in work teams. Furthermore, the study examined the Job Demands and Resources model (JD-R) including the relationship with the work family balance (WFB) of public employees. The sample was composed of 404 technical and administrative staff in a Spanish public university. The results indicated the significant relationships between the perceptions of IJC and burnout, engagement, and the two work outcomes WFB and ERP. When burnout and engagement were introduced in the regression equations, total mediation effects were produced.