Federated Unsupervised Learning (FUL) aims to learn expressive representations in federated and self-supervised settings. The quality of representations learned in FUL is usually determined by uniformity, a measure of how uniformly representations are distributed in the embedding space. However, existing solutions perform well in achieving intra-client (local) uniformity for local models while failing to achieve inter-client (global) uniformity after aggregation due to non-IID data distributions and the decentralized nature of FUL. To address this issue, we propose Soft Separation and Distillation (SSD), a novel approach that preserves inter-client uniformity by encouraging client representations to spread toward different directions. This design reduces interference during client model aggregation, thereby improving global uniformity while preserving local representation expressiveness. We further enhance this effect by introducing a projector distillation module to address the discrepancy between loss optimization and representation quality. We evaluate SSD in both cross-silo and cross-device federated settings, demonstrating consistent improvements in representation quality and task performance across various training scenarios. Our results highlight the importance of inter-client uniformity in FUL and establish SSD as an effective solution to this challenge.