When a robot is said to be a specialist in a particular domain, does it alter the nature and quality of human-robot interaction? This study examines the effects of specialization in robot functions, along with individual difference in immersive tendencies, on users' trust, perception, activity, and memory. In a controlled experiment, 38 participants were taught a physical exercise lesson from either a specialist or generalist humanoid robot for 6 min. Results showed that specialization had effects on the participants' affective trust; and immersive tendency predicted active participation in the interaction and led to better memory. The latter also moderated the effect of the former - users with higher immersive tendency are more likely to make human attributions of specialization, and rate a specialist robot as more intelligent than a generalist robot. These results have theoretical implications for media-equation as well as design implications for human-robot interaction professionals.