Concerns about child physical and digital safety are emerging with families' adoption of smart home technologies such as robot vacuums and smart speakers. To better understand parents' definitions and perceptions of child safety regarding smart home technologies, we interviewed 23 parents who are smart home adopters. We contribute insights into parents' perceptions of the physical and digital safety risks smart home technologies pose to children, and how such perceptions formed and changed across three phases. In acquiring smart home devices, parents already considered whether the device could cause physical harm to their children or pose privacy and security risks. Once children become active users of smart home technologies, parents however reported encountering unanticipated physical safety risks and digital safety issues (e.g., exposure to unsuitable content) that required their mitigation strategies. As their children grow up, parents further expressed the need to shift attention from physical safety to digital safety. Parents' safety perceptions influence how they involve children in smart home interactions and implement mitigation strategies, such as restricting access to certain devices and using parental controls. We identify six factors that shape parents' perception and evaluation of smart home safety risks to children, including parenting style, parents' tech-savviness, parents' trust in tech companies, children's age and developmental differences, news media, and device characteristics. We provide design and policy recommendations to better protect children's safety in the smart home environment. CCS Concepts: • Security and privacy → Social aspects of security and privacy; Usability in security and privacy; • Human-centered computing → Ubiquitous and mobile devices; • Social and professional topics → Children.