While the next generation mobile network, 6G, will bring new capabilities and benefits for mobile network users and operators, it will also increase the network’s complexity in management and orchestration. To address this challenge, integrating the digital twin (DT) concept into the 6G architecture has been proposed to help manage the increased complexity. However, this integration may introduce new vulnerabilities. Therefore, this study aims to identify the vulnerabilities and threats specific to the data management framework for the network digital twin (NDT) enabled 6G architecture. NDT is investigated with a focus on its security and privacy aspects, particularly from a data management perspective, through a thorough review of the currently proposed architecture. Additionally, specific threats and countermeasures to data management are identified to enable developing a 6G architecture that securely integrates the NDT framework. Moreover, the feasibility of the countermeasures is discussed for ensuring secure real-time network management, optimization, and decision-making.