Semantic ID-based generative retrieval represents each item with a short sequence of discrete tokens derived from language-based item representations. Existing methods mainly instantiate this idea in two paradigms: autoregressive SID generation and parallel SID generation. In both paradigms, the quality of Semantic IDs depends critically on how continuous item embeddings are discretized before they become generation targets. While existing work has improved SID tokenization through better quantization objectives and supervision signals, it often treats the pre-tokenization embedding space as fixed, overlooking that pretrained item embeddings can be anisotropic and dominated by a few directions. This creates a pre-quantization distribution mismatch, where the global embedding geometry may not align with the structured spaces used for code assignment. We propose GeoSID, a tokenizer-side geometric shaping framework that keeps the downstream generative recommender unchanged. GeoSID uses a lightweight projected distribution matching regularizer to adjust item representations before SID assignment, and places the shaping objective in tokenizer-specific quantization spaces, including residual levels for residual quantization and OPQ/PQ blocks for product quantization. On the RPG backbone, GeoSID achieves up to 8.13% relative improvement in Recall@10 and 6.91% in NDCG@10. Further analyses show that GeoSID reduces projected distribution discrepancy, improves code usage balance, and lowers prefix-level SID collisions. Code is available at https://github.com/hexinrong122/GeoSID.