Automation tools like continuous integration services, code coverage reporters, style checkers, dependency managers, etc. are all known to provide significant improvements in developer productivity and software quality. Some of these tools are widespread, others are not. How do these automation "best practices" spread? And how might we facilitate the diffusion process for those that have seen slower adoption? In this paper, we rely on a recent innovation in transparency on code hosting platforms like GitHub---the use of repository badges---to track how automation tools spread in open-source ecosystems through different social and technical mechanisms over time. Using a large longitudinal data set, multivariate network science techniques, and survival analysis, we study which socio-technical factors can best explain the observed diffusion process of a number of popular automation tools. Our results show that factors such as social exposure, competition, and observability affect the adoption of tools significantly, and they provide a roadmap for software engineers and researchers seeking to propagate best practices and tools.