Scanpath prediction in omnidirectional images (ODIs) serves as a critical component for optimizing foveated rendering efficiency and enhancing interactive quality in virtual reality systems. However, existing scanpath prediction methods for ODIs still suffer from fundamental limitations: (1) inadequate modeling and capturing of long-range temporal dependencies in fixation regions, and (2) suboptimal integration of spatial and temporal visual features, ultimately compromising prediction performance. To address these limitations, we propose a novel Dual-Temporal Modulated Diffusion model for Omnidirectional Images Scanpath Prediction, named SalDiff-DTM model, to effectively generate realistic human eye viewing trajectories. Specifically, to effectively model spatial relationships, we propose a novel Dual-Graph Convolutional Network (Dual-GCN) module that simultaneously captures semantic-level and image-level correlations. By integrating both local spatial details and global contextual information across the internal temporal dimension, this module achieves comprehensive and robust modeling of spatial relationships. To further enhance the modeling of temporal dependencies inherent in diverse fixation patterns, we introduce TABiMamba (Temporal-Aware BiLSTM-Mamba), a dedicated module that synergistically combines the contextual sensitivity of BiLSTM with the long-range sequence modeling capabilities of Mamba. This design facilitates deep information flow and context-aware sequential reasoning, thereby enabling high-fidelity capture of intricate temporal correlations. Inspired by the progressive refinement mechanism of diffusion models in various generative tasks, we propose a saliency-guided diffusion module that formulates the prediction problem as a conditional generative process, iteratively yielding accurate and perceptually plausible scanpaths. Extensive experiments demonstrate that SalDiff-DTM significantly outperforms state-of-the-art models, paving the way for future advancements in eye-tracking technologies and cognitive modeling, while broadening the horizons for immersive VR development.