Next Point-of-Interest (POI) recommendation is a research hotspot in business intelligence, where users' spatial-temporal transitions and social relationships play key roles. However, most existing works model spatial and temporal transitions separately, leading to misaligned representations of the same spatial-temporal key nodes. This misalignment introduces redundant information during fusion, increasing model uncertainty and reducing interpretability. To address this issue, we propose DiMuST, a socially enhanced POI recommendation model based on disentangled representation learning over multiplex spatial-temporal transition graphs. The model employs a novel Disentangled variational multiplex graph Auto-Encoder (DAE), which first disentangles shared and private distributions using a multiplex spatial-temporal graph strategy. It then fuses the shared features via a Product of Experts (PoE) mechanism and denoises the private features through contrastive constraints. The model effectively captures the spatial-temporal transition representations of POIs while preserving the intrinsic correlation of their spatial-temporal relationships. Experiments on two challenging datasets demonstrate that our DiMuST significantly outperforms existing methods across multiple metrics.