AI-enabled smart-home agents that automate household routines are increasingly viable, but the design space of how and what such systems should communicate with their users remains underexplored. Through a user-enactment study, we identified various interpretations of and feelings toward such a system's confidence in its automated acts. That confidence and their own mental models influenced what and how the participants wanted the system to communicate, as well as how they would assess, diagnose, and subsequently improve it. Automated acts resulted from false predictions were not generally considered improper, provided that they were perceived as reasonable or potentially useful. The participants' improvement strategies were of four general types, all of which will be discussed. Factors affecting their preferred levels of involvement in automated acts and their interest in system confidence were also identified. We conclude by making practical design recommendations for the user-system communication design spaces of smart-home routine assistants.