Federated class-incremental learning (FCIL) aims to incrementally learn new classes across decentralized clients under non-IID data distributions. However, the pervasive challenge of label noise in FCIL has been completely overlooked. In this work, we introduce federated noisy class-incremental learning (FNCIL) and, for the first time, identify a novel form of label noise—spatio-temporal label misalignment—where samples from unseen classes are entirely mislabeled as known classes, with their correctly labeled counterparts appearing in latter tasks or other clients. This phenomenon undermines the effectiveness of existing centralized denoising strategies and creates a clear requirement for noise-robust methods in real-world FNCIL scenarios. To tackle this issue, we propose FedRNC, a dual-phase framework that leverages feature-space associations to establish spatio-temporal correspondences between clean global prototypes and noisy cached samples for progressive label correction. Experiments on standard benchmarks demonstrate FedRNC's superiority against existing baselines, along with its plug-and-play capability to upgrade FCIL systems for FNCIL.