Video frame interpolation (VFI) that leverages the bio-inspired event cameras as guidance has recently shown better performance and memory efficiency than the frame-based methods, thanks to the event cameras' advantages, such as high temporal resolution. A hurdle for event-based VFI is how to effectively deal with non-linear motion, caused by the dynamic changes in motion direction and speed within the scene. Existing methods either use events to estimate sparse motion fields or fuse events with image features to estimate dense motion fields. Unfortunately, motion errors often degrade the VFI quality as the continuous motion cues from events does not align with the dense spatial information of images in the temporal dimension. In this paper, we find that object motion is continuous in space, tracking local regions over continuous time enables more accurate identification of spatiotemporal feature correlations. In light of this, we propose a novel continuous point tracking-based VFI framework, named TimeTracker. Specifically, we first design a Scene-Aware Region Segmentation (SARS) module to divide the scene into similar patches. Then, a Continuous Trajectory guided Motion Estimation (CTME) module is proposed to track the continuous motion trajectory of each patch through events. Finally, intermediate frames at any given time are generated through global motion field optimization and frame refinement. Moreover, we collect a real-world dataset that features fast non-linear motion. Extensive experiments show that our method outperforms prior arts in both motion estimation and frame interpolation quality.