With millions of connected edge gateways, there is a pressing challenge of remote maintenance of containerised software components after the initial release. To support remote update operations, edge software providers have been increasingly adopting digital twin-based device management platforms for run-time monitoring and interaction. A common limitation of these solutions is the lack of support for modelling the multi-dimensional context of edge devices deployed in the field, which hinders the software management in a tailored and context-aware manner. This paper aims to address this lack of context-awareness in digital twins required for edge software assignment by introducing two modelling principles, which allow focusing on the device fleet as a whole and capturing the diverse cyber-physical-social context of individual devices. As part of proof of concept, these principles were incorporated in an existing digital twin platform. This prototype implementation demonstrates the viability of the proposed modelling principles via a running example in the context of a telemedicine application system.