In this article, we present a novel user-centric service provision for immersive communications (IC) in 6G to deal with the uncertainty of individual user behaviors while satisfying unique requirements on the quality of multi-sensory experience. To this end, we propose a data-oriented approach for network resource management, featuring personalized data management that can support network modeling tailored to different user demands. Our approach leverages the digital twin (DT) technique as a key enabler. Particularly, a DT is established for each user, and the data attributes in the DT are customized based on the characteristics of the user. The DT functions, corresponding to various data operations, are customized in the development, evaluation, and update of network models to meet unique user demands. A trace-driven case study demonstrates the effectiveness of our approach in achieving user-centric IC and the significance of personalized data management in 6G.