Differentiated instruction is much demanded yet quite challenging in face of the growing student diversity in today's K-12 classrooms. One major challenge is the provision of differentiated materials to students. Automated text simplification (ATS) tools fueled by natural language processing may serve as a useful assistant for teachers. However, little is known about teachers' contextualized use of ATS over time. This case study traced two teachers' use of ATS systems over a semester. Drawing upon three semi-structured interviews and teacher-generated materials with ATS, we identified an evolving pattern of teachers' engagement with ATS systems, a progression from a blind reliance on the tool to a more critical and coordinated use of the tool over time. We further revealed that teachers' evolving understanding of DI, positioning of the role of ATS systems and human instructors, and interpretation of DI need in specific teaching situations interplayed to shape their particular ways of engagement. Overall, this study contributes to the understanding of teachers' contextualized use of ATS technology for DI. By revealing the influencing factors, the findings hold significant pedagogical implications to inform the design of ATS tools and the creation of favorable conditions to maximize the potential of ATS tools for DI and language teaching and learning in general.