The complementary integration of artificial intelligence (AI) in the workplace requires balancing performance goals with psychological needs, as both are essential for sustained outcomes. This study examines different workflows (AI-first and human-first) as cognitive forcing strategies to test whether they enhance performance and psychological outcomes compared to human-only and AI-only processing. In a one-factorial between-subjects experiment (N = 101) within a visual inspection task, evaluated at up to three measurement points, performance variables (accuracy, speed, error rates) and psychological variables (vigilance, flow, teaming experience, wellbeing when working with the AI) were assessed. Human-AI collaboration outperformed AI-only in error rates (η2 = 0.29) and human-only in speed (η2 = 0.11 - 0.14), but only when AI preceded human processing. The AI-first workflow enhanced teaming perception compared to human-only processing (η2 = 0.07). Moreover, human-AI collaborative processing reduced flow decrease compared to human-only processing (η2 = 0.07). Overall, AI processing preceding human processing produces the best balance between performance and psychological outcomes in safety-critical inspection tasks, supporting a holistic view of AI integration in the workplace.