Management factors are among the most significant causes of construction safety incidents, and there is an issue of insufficient supervision at present. The degree of diligence exhibited by relevant entities is crucial, and the payoff can influence the decision-making behaviors of involved parties. Based on this, the aim of this paper is to investigate how to enhance the initiative of enterprises in fulfilling their safety responsibilities during the construction process. By developing a tripartite evolutionary game model that involves supervision companies, general contractors, and labor subcontractors and conducting numerical simulation analysis, we reveal that simultaneous proactive investment in safety by all three parties is challenging, with labor subcontractors being relatively more prone to opt for active safety investment. Supervision companies and general contractors often struggle to fulfill their safety duties at the same time. Factors such as the rewards and penalties stipulated in a contract, rent-seeking amounts, and accident-related losses have a significant impact on the evolution of the system. Based on the findings, we propose recommendations for construction management, which include the management of labor subcontracting in construction, the control of rent-seeking behaviors, and the establishment of a cooperative safety culture during the construction process.