Tibetan's low-resource status has hindered its digital preservation, particularly in Handwritten Character Recognition (HCR). The field lacks foundational models aligned with modern technological advances as well as effective data augmentation methods. For online HCR, the primary challenge is appropriately leveraging temporal information. To address these challenges, we propose TSTN, a spatiotemporal network model tailored for Tibetan online HCR. TSTN excels at capturing both temporal and spatial features from online samples. Using the MRG-OHTC dataset with 583 Tibetan characters, experimental results demonstrate TSTN's superiority, achieving a highest accuracy of 89.26% and a stable average accuracy of 85.13%. To further mitigate data scarcity, we implement geometric data augmentation to enhance accuracy and validate TSTN's robustness in trajectory sequence feature extraction. Furthermore, we generate new samples by segmenting and recombining Tibetan character components, demonstrating the reliability and effectiveness of this approach in boosting recognition performance. Our structureaware data augmentation SplitMix methods further improve performance by a maximum of 1.75%. Our code will be made publicly available soon.