Digital Twins (DTws) are a powerful platform for facilitating industrial automation, enabling the digitization, integration, and real-time synchronization of processes within industry environments. A proactive data governance and management strategy ensures the robustness, fidelity and viability of DTws This paper addresses the critical requirement for data governance, a pillar necessary for implementing DTws, focusing specifically on compliance with the international ISO 23247 standard. To facilitate the transition, we propose and detail a governance-driven reference architecture designed for DTws. This flexible model integrates governance controls that ensure comprehensive traceability, real-time responsiveness, and examinable feedback loops across operational technology (OT) and information technology (IT) networks. Our analysis concludes that the successful adoption of DTw-enabled manufacturing hinges on a prior organizational assessment of data governance maturity. We demonstrate that adherence to an ISO 23247-compliant architectural structure is not only a matter of compliance but is essential to guarantee the truthfulness and reliability of the digital representation, thereby enabling continuous improvement in industrial processes.