Integrated Development Environments increasingly implement AI-powered code completion tools (CCTs), which promise to enhance developer efficiency, accuracy, and productivity. However, interaction challenges with CCTs persist, mainly due to mismatches between developers' mental models and the unpredictable behavior of AI-generated suggestions, which is an aspect underexplored in the literature. We conducted an elicitation study with 56 developers using co-design workshops to elicit their mental models when interacting with CCTs. Different important findings that might drive the interaction design with CCTs emerged. For example, developers expressed diverse preferences on when and how code suggestions should be triggered (proactive, manual, hybrid), where and how they are displayed (inline, sidebar, popup, chatbot), as well as the level of detail. It also emerged that developers need to be supported by customization of activation timing, display modality, suggestion granularity, and explanation content, to better fit the CCT to their preferences. To demonstrate the feasibility of these and the other guidelines that emerged during the study, we developed ATHENA, a proof-of-concept CCT that dynamically adapts to developers' coding preferences and environments, ensuring seamless integration into diverse workflows.