Maternal mind-mindedness is known to be a tendency of caregivers to interpret their socially immature infants as social agents and researchers have indicated this is one of promotion factors of infant social development. In this paper, we focused on such caregiver's tendency in mutual imitation of vowels and modeled infant vowel development to investigate the effect of caregivers on infant development. Computational simulation results in our previous study of caregiver-infant mutual imitation showed what we call auto-mirroring bias of the caregiver has a guiding effect in vowel development. This hypothesized bias is the tendency to interpret infant's utterances as more accurate imitations of the caregiver's precedent utterances and considered to be one of behaviors of the mind-mindedness. To verify this bias, we further examined how adult's interpretation was biased by measuring their imitations of synthesized vowels. The result of this subject experiment indicated the bias was enhanced by the anticipation to be imitated. These results of our studies imply the possibility that the way caregiversimitate their infant based on their interpretation of their infants lets them learn caregiver's way of interpreting others, i.e. sociality.