As human-robot interactions become more social, a robot's personality plays an increasingly vital role in shaping user experience and its overall effectiveness. In this study, we examine the impact of three distinct robot personalities on user experiences during well-being exercises: a Baseline Personality that aligns with user expectations, a High Extraversion Personality, and a High Neuroticism Personality. These personalities were manifested through the robot's dialogue, which were generated using a large language model (LLM) guided by key behavioral characteristics from the Big 5 personality traits. In a between-subjects user study (N = 66), where each participant interacted with one distinct robot personality, we found that both the High Extraversion and High Neuroticism Robot Personalities significantly enhanced participants' emotional states (arousal, control, and valence). The High Extraversion Robot Personality was also rated as the most enjoyable to interact with. Additionally, evidence suggested that participants' personality traits moderated the effectiveness of specific robot personalities in eliciting positive outcomes from well-being exercises. Our findings highlight the potential benefits of designing robot personalities that deviate from users' expectations, thereby enriching human-robot interactions.