Multi-object tracking in video often requires appearance or location cues that can reveal sensitive identity information, while adding privacy-preserving noise typically disrupts cross-frame association and causes ID switches or target loss. We propose TSDCRF, a plug-in refinement framework that balances privacy and tracking by combining three components: (i) $(\varepsilon,δ)$-differential privacy via calibrated Gaussian noise on sensitive regions under a configurable privacy budget; (ii) a Normalized Control Penalty (NCP) that down-weights unstable or conflicting class predictions before noise injection to stabilize association; and (iii) a time-series dynamic conditional random field (DCRF) that enforces temporal consistency and corrects trajectory deviation after noise, mitigating ID switches and resilience to trajectory hijacking. The pipeline is agnostic to the choice of detector and tracker (e.g., YOLOv4 and DeepSORT). We evaluate on MOT16, MOT17, Cityscapes, and KITTI. Results show that TSDCRF achieves a better privacy--utility trade-off than white noise and prior methods (NTPD, PPDTSA): lower KL-divergence shift, lower tracking RMSE, and improved robustness under trajectory hijacking while preserving privacy. Source code in https://github.com/mabo1215/TSDCRF.git