The routine assessment of workplace stress is mostly based on standardized self-report tools, including generic psychosocial risk indicators (G-PRIs) designed to fit very heterogeneous occupational sectors. However, the use “by default” of such indicators might be inadequate when they fail to characterize the specificity of the work environment; hence, the inclusion of more contextualized indicators (C-PRIs) has been recommended. We aimed at evaluating the additional contribution of three C-PRIs (Work–Family Conflict, Emotional Demands, and Excessive Demands from Patients) in predicting individual outcomes (Emotional Exhaustion, Turnover Intentions) compared to commonly used G-PRIs (e.g., Demand, Control, Support), in a sample of 787 healthcare workers involved in a routine workplace stress assessment. Multilevel hierarchical regression supported the additional contributions of C-PRIs in predicting both outcomes over G-PRIs, sex, age and shift work. More robust and consistent evidence emerged for Emotional Exhaustion, which was significantly predicted by all C-PRIs, whereas Turnover Intentions was only predicted by the C-PRI Emotional Demands. Importantly, not all G-PRIs showed a relationship with the two outcomes. Taken together, our results support the importance of including C-PRIs in workplace stress assessment carried out by organizations, which should be selected based on literature search and discussion with the stakeholders.