(1) Background: The objective of this manuscript is to propose the necessity of job demands to ensure the positive influence of policies in stimulating employees’ engagement and performance. If the policies related to the intellectual stimulation of employees implemented by team leaders are to have positive effects on employee performance, they must induce emotional engagement in the employees. Furthermore, to achieve this positive influence on emotions, the organization must offer an environment that challenges the employees in the organization. Here, we analyze a moderate mediation model to examine the moderating, positive effect of role conflict on the intellectual engagement and performance of employees. (2) Methods: This study involved 705 employees of a multinational private company based in Spain. (3) Results: We confirm the positive moderating effect of role conflict between the intellectual stimulation of employees and intellectual engagement, and the mediating effect of intellectual engagement between leadership behavior and employee performance. (4) Conclusions: Organizational leader stimulation practices necessitate an environment of moderate job demands in order to improve the intellectual engagement of employees, thereby increasing their performance. The implications of the findings in terms of theory, research and practice are discussed.