The rise of AI user applications opened avenues for innovative research on the way humans and AI interact. However, the lack of univocal guidelines on the properties of this cutting-edge technology invites thorough attention, should we want to augment the behavioural response. In particular, there is a need to find a right balance between algorithmic inferences and humanised agency. Current paper embraced these challenges to provide the very-needed understanding. Based on profound literature audit, factors emerging as crucial drivers of user perception of AI agency, and consequent behavioural response were tested in empirical study. We zoomed-in into AI properties hypothesised to impact the human-AI interaction such as personalness, humanlikeness, helpfulness, competence, and explainability. Results are clear in showing that consumers in high satisfaction group provided more favourable evaluation, in comparison to those in low satisfaction group. There was a strong and positive correlation between AI properties recognised as key drivers of behavioural response. Current outcomes are discussed in the framework of HumanAIse system. High human touch, personalness, and helpfulness were greatly appreciated by our respondents, and therefore, demonstrating the consumer desire for humanAIsed interaction. Present work provides insightful knowledge on core AI properties that could be employed to build such human-AI interaction wanted by consumers, that might lift the satisfaction, and thus, augmenting the behavioural response.