Brain tumor segmentation is critical in diagnosis and treatment planning for the disease. Yet, current deep learning methods rely on centralized data collection, which raises privacy concerns and limits generalization across diverse institutions. In this paper, we propose TwinSegNet, which is a privacy-preserving federated learning framework that integrates a hybrid ViT-UNet model with personalized digital twins for accurate and real-time brain tumor segmentation. Our architecture combines convolutional encoders with Vision Transformer bottlenecks to capture local and global context. Each institution fine-tunes the global model of private data to form its digital twin. Evaluated on nine heterogeneous MRI datasets, including BraTS 2019-2021 and custom tumor collections, TwinSegNet achieves high Dice scores (up to 0.90%) and sensitivity/specificity exceeding 90%, demonstrating robustness across non-independent and identically distributed (IID) client distributions. Comparative results against centralized models such as TumorVisNet highlight TwinSegNet's effectiveness in preserving privacy without sacrificing performance. Our approach enables scalable, personalized segmentation for multi-institutional clinical settings while adhering to strict data confidentiality requirements.