The primate visual cortex exhibits topographic organization, where functionally similar neurons are spatially clustered, a structure widely believed to enhance neural processing efficiency. While prior works have demonstrated that conventional deep ANNs can develop topographic representations, these models largely neglect crucial temporal dynamics. This oversight often leads to significant performance degradation in tasks like object recognition and compromises their biological fidelity. To address this, we leverage spiking neural networks (SNNs), which inherently capture spike-based temporal dynamics and offer enhanced biological plausibility. We propose a novel Spatio-Temporal Constraints (STC) loss function for topographic deep spiking neural networks (TDSNNs), successfully replicating the hierarchical spatial functional organization observed in the primate visual cortex from low-level sensory input to high-level abstract representations. Our results show that STC effectively generates representative topographic features across simulated visual cortical areas. While introducing topography typically leads to significant performance degradation in ANNs, our spiking architecture exhibits a remarkably small performance drop (No drop in ImageNet top-1 accuracy, compared to a 3% drop observed in TopoNet, which is the best-performing topographic ANN so far) and outperforms topographic ANNs in brain-likeness. We also reveal that topographic organization facilitates efficient and stable temporal information processing via the spike mechanism in TDSNNs, contributing to model robustness. These findings suggest that TDSNNs offer a compelling balance between computational performance and brain-like features, providing not only a framework for interpreting neural science phenomena but also novel insights for designing more efficient and robust deep learning models.