In recent years, Temporal Knowledge Graph (TKG) reasoning has made progress in modeling periodic events. However, it still faces challenges in reasoning about emergent and aperiodic events, traditional methods fail to effectively model the topological dependencies inherent in the dynamic evolution of non-periodic events, due to inadequate spatio-temporal correlation modeling. To mitigate these challenges, this paper proposes WaveDSTG, a novel multiscale wavelet transform and spatio-temporal attention-driven TKG reasoning model. By collaboratively encoding multiscale temporal features through wavelet transform and fourier basis, it effectively captures both periodic and non-periodic events, thus overcoming the limitations of single-scale modeling. Meanwhile, the proposed model incorporates spatio-temporal dynamic attention with a dual-projection contrastive learning mechanism to construct both historical and non-historical subgraphs, which are independently utilized for dual-path prediction. By leveraging contrastive objectives in conjunction with orthogonal regularization, the model effectively disentangles spatio-temporal representations, enabling more structured and discriminative feature learning. Experimental results show that WaveDSTG outperforms other similar models in terms of effectiveness and efficiency on four TKG benchmarks.