AI-driven conversational coaching is increasingly used to support workplace negotiation, yet prior work assumes uniform effectiveness across users. We challenge this assumption by examining how individual differences, particularly personality traits, moderate coaching outcomes. We conducted a between-subjects experiment (N=267) comparing theory-driven AI (Trucey), general-purpose AI (Control-AI), and a traditional negotiation handbook (Control-NoAI). Participants were clustered into three profiles -- resilient, overcontrolled, and undercontrolled -- based on the Big-Five personality traits and ARC typology. Resilient workers achieved broad psychological gains primarily from the handbook, overcontrolled workers showed outcome-specific improvements with theory-driven AI, and undercontrolled workers exhibited minimal effects despite engaging with the frameworks. These patterns suggest personality as a predictor of readiness beyond stage-based tailoring: vulnerable users benefit from targeted rather than comprehensive interventions. The study advances understanding of personality-determined intervention prerequisites and highlights design implications for adaptive AI coaching systems that align support intensity with individual readiness, rather than assuming universal effectiveness.