Temporal misalignment (time offset) between sensors is common in low cost visual-inertial odometry (VIO) systems. Such temporal misalignment introduces inconsistent constraints for state estimation, leading to a significant positioning drift especially in high dynamic motion scenarios. In this article, we focus on online temporal calibration to reduce the positioning drift caused by the time offset for high dynamic motion VIO. For the time offset observation model, most existing methods rely on accurate state estimation or stable visual tracking. For the prediction model, current methods oversimplify the time offset as a constant value with white Gaussian noise. However, these ideal conditions are seldom satisfied in real high dynamic scenarios, resulting in the poor performance. In this paper, we introduce online time offset modeling networks (TON) to enhance real-time temporal calibration. TON improves the accuracy of time offset observation and prediction modeling. Specifically, for observation modeling, we propose feature velocity observation networks to enhance velocity computation for features in unstable visual tracking conditions. For prediction modeling, we present time offset prediction networks to learn its evolution pattern. To highlight the effectiveness of our method, we integrate the proposed TON into both optimization-based and filter-based VIO systems. Simulation and real-world experiments are conducted to demonstrate the enhanced performance of our approach. Additionally, to contribute to the VIO community, we will open-source the code of our method on: https://github.com/Franky-X/FVON-TPN.