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Digital Twin (DT) aims to provide industrial companies with an interface to visualize, analyze, and simulate the production process, improving overall performance. This paper proposes to extend existing DT by adding a complementary methodology to make it suitable for process supervision. To implement our methodology, we introduce a novel framework that identifies, collects, and analyses data from the production system, enhancing DT functionalities. In our case study, we implemented Key Performance Indicators (KPIs) in the immersive environment to monitor physical processes through cyber representation. First, a review of the Digital Twin (DT) allows us to understand the status of the existing methodologies as well as the problem of data contextualization in recent years. Based on this review, performance data in Cyber–Physical Systems (CPS) are identified, localized, and processed to generate indicators for monitoring machine and production line performance through DT. Finally, a discussion reveals the difficulties of integration and the possibilities to respond to other major industrial challenges, like predictive maintenance.