Understanding human actions from videos plays a critical role across various domains, including sports analytics. In figure skating, accurately recognizing the type and timing of jumps a skater performs is essential for objective performance evaluation. However, this task typically requires expert-level knowledge due to the fine-grained and complex nature of jump procedures. While recent approaches have attempted to automate this task using Temporal Action Segmentation (TAS), there are two major limitations to TAS for figure skating: the annotated data is insufficient, and existing methods do not account for the inherent three-dimensional aspects and procedural structure of jump actions. In this work, we propose a new TAS framework for figure skating jumps that explicitly incorporates both the three-dimensional nature and the semantic procedure of jump movements. First, we propose a novel View-Invariant, Figure Skating-Specific pose representation learning approach (VIFSS) that combines contrastive learning as pre-training and action classification as fine-tuning. For view-invariant contrastive pre-training, we construct FS-Jump3D, the first publicly available 3D pose dataset specialized for figure skating jumps. Second, we introduce a fine-grained annotation scheme that marks the ``entry (preparation)'' and ``landing'' phases, enabling TAS models to learn the procedural structure of jumps. Extensive experiments demonstrate the effectiveness of our framework. Our method achieves over 92% F1@50 on element-level TAS, which requires recognizing both jump types and rotation levels. Furthermore, we show that view-invariant contrastive pre-training is particularly effective when fine-tuning data is limited, highlighting the practicality of our approach in real-world scenarios.