Prompt-based personality control is a key technique for designing large language model (LLM) dialogue agents that behave consistently across social contexts. However, specifying Big Five personality traits (BFTs) in a prompt does not ensure that the intended traits are expressed in generated utterances. This paper investigates this mismatch from an interactionist perspective, viewing personality expression as a context-dependent outcome shaped by the interplay between trait specification and situational factors. We analyze how perceived BFT expression in LLM-generated dialogue is influenced by three prompt factors: personality traits, dialogue roles, and expressive styles. Using a factorial design that combines six personality conditions, three roles, and three expressive-style conditions, we generate 1,080 LLM-agent dialogues in each of English and Japanese. We then evaluate the target agent's utterances using an LLM-as-a-judge framework to estimate expressed Big Five traits. The results show that expressed personality is shaped not only by explicit trait specification, but also by dialogue role and expressive style. These effects are trait-specific: dialogue role strongly influences Openness, expressive style substantially shapes Conscientiousness and Agreeableness, and explicit trait specification dominates Neuroticism. Even without explicit personality-trait specification, social and expressive conditions induce distinct personality-like impressions. Cross-linguistic comparisons show broadly similar patterns between English and Japanese dialogues, with noticeable differences only under specific combinations of personality, role, and expressive style. These findings suggest that personality control in LLM agents should be understood not as a direct consequence of trait prompting, but as a context-dependent process involving personality specification, social role, and expressive style.