It is now common for people to encounter artificial intelligence (AI) across many areas of their personal and professional lives. Interactions with AI agents may range from the routine use of information technology tools to encounters where people perceive an artificial agent as exhibiting mind. Combining two studies (useable N = 266), we explore people's qualitative descriptions of a personal encounter with an AI in which it exhibits characteristics of mind. Across a range of situations reported, a clear pattern emerged in the responses: the majority of people report their own emotions including surprise, amazement, happiness, disappointment, amusement, unease, and confusion in their encounter with a minded AI. We argue that emotional reactions occur as part of mind perception as people negotiate between the disparate concepts of programmed electronic devices and actions indicative of human-like minds. Specifically, emotions are often tied to AIs that produce extraordinary outcomes, inhabit crucial social roles, and engage in human-like actions. We conclude with future directions and the implications for ethics, the psychology of mind perception, the philosophy of mind, and the nature of social interactions in a world of increasingly sophisticated AIs.