Digital twin applications use digital artefacts to twin physical systems. The purpose is to continuously mirror the structure and behavior of the physical system, such that users can analyse the physical system by means of the digital twin. However, the physical system might change over time. In this case, the digital twin’s ensemble of digital artefacts needs to be reconfigured to correctly twin the physical system again. This paper considers a digital twin infrastructure combining MAPE-K feedback loops and semantic reflection to automatically ensure that the digital artefacts correctly twin the physical system; i.e., the resulting system is twinned-by-construction. We consider the monitoring of both structural and temporal correctness properties for digital twin, including the time delay required by reconfiguration, and the capture of execution traces to reflect digital threads in the digital twin framework.