Incomplete multimodal sentiment analysis has attracted increasing research interest in recent years. Existing methods attempt to recover missing modalities through generative reconstruction and text-enhanced fusion, but these approaches may be limited in preserving sentiment-relevant information and fully leveraging complementary and hierarchical cross-modal interactions, particularly under noisy or incomplete conditions. To address these challenges, we propose TC-DSC, a text-centric hierarchical dual-stream interaction framework for incomplete multimodal sentiment analysis. Rather than reconstructing raw signals, TC-DSC performs semantic alignment and consistency modeling in the feature space through structured interactions between a text-centric stream and auxiliary audio-visual streams. A multi-scale enhanced encoder is designed to improve the robustness of non-text modalities under noisy conditions. Furthermore, a hierarchical proxy layer enables bidirectional interaction, with the text modality serving as a semantic anchor to guide cross-modal alignment. A semantic distillation strategy is also incorporated to facilitate knowledge transfer in the feature space under modality missing. Extensive experiments on MOSI, MOSEI, and SIMS demonstrate that TC-DSC achieves competitive performance and consistent improvements under both complete and incomplete settings.