In case of a major social crisis, such as the coronavirus pandemic, the most important measure is to identify the determinants influencing employee health and well-being, which are directly linked to workplace job performance. Many studies have explored the role of employee engagement in the relationship between job resources, psychological capital, and job performance; however, only a few have investigated the relationships reflecting rapid changes in the work environment represented by digital transformation and a major social crisis. Considering this, this study examines how job autonomy and psychological well-being, which lower employee anxiety about health and welfare, influence in-role performance in the form of proactive employee characteristics as well as extra-role performance in the form of prosocial behavior, as mediated by employee engagement. The results of the data analysis of 1,092 corporate employees in Korea supported this model. Specifically, job autonomy and psychological well-being influence job performance (i.e., personal initiative and prosocial behavior) through improvements in employee engagement. Based on these findings, the study also discusses the implications of the results, future directions, and limitations.