Human Immunodeficiency Virus (HIV) has posed a major global health challenge for decades, and forecasting HIV diagnoses continues to be a critical area of research. However, capturing the complex spatial and temporal dependencies of HIV transmission remains challenging. Conventional Message Passing Neural Network (MPNN) models rely on a fixed binary adjacency matrix that only encodes geographic adjacency, which is unable to represent interactions between non-contiguous counties. Our study proposes a deep learning architecture Mobility-Aware Transformer-Message Passing Neural Network (MAT-MPNN) framework to predict county-level HIV diagnosis rates across California, Florida, and the New England region. The model combines temporal features extracted by a Transformer encoder with spatial relationships captured through a Mobility Graph Generator (MGG). The MGG improves conventional adjacency matrices by combining geographic and demographic information. Compared with the best-performing hybrid baseline, the Transformer MPNN model, MAT-MPNN reduced the Mean Squared Prediction Error (MSPE) by 27.9% in Florida, 39.1% in California, and 12.5% in New England, and improved the Predictive Model Choice Criterion (PMCC) by 7.7%, 3.5%, and 3.9%, respectively. MAT-MPNN also achieved better results than the Spatially Varying Auto-Regressive (SVAR) model in Florida and New England, with comparable performance in California. These results demonstrate that applying mobility-aware dynamic spatial structures substantially enhances predictive accuracy and calibration in spatiotemporal epidemiological prediction.