Unified Multimodal understanding and generation Models (UMMs) have demonstrated remarkable capabilities in both understanding and generation tasks. However, we identify a vulnerability arising from the generation-understanding coupling in UMMs. The attackers can use the generative function to craft an information-rich adversarial image and then leverage the understanding function to absorb it in a single pass, which we call Cross-Modal Generative Injection (CMGI). Current attack methods on malicious instructions are often limited to a single modality while also relying on prompt rewriting with semantic drift, leaving the unique vulnerabilities of UMMs unexplored. We propose STaR-Attack, the first multi-turn jailbreak attack framework that exploits unique safety weaknesses of UMMs without semantic drift. Specifically, our method defines a malicious event that is strongly correlated with the target query within a spatio-temporal context. Using the three-act narrative theory, STaR-Attack generates the pre-event and the post-event scenes while concealing the malicious event as the hidden climax. When executing the attack strategy, the opening two rounds exploit the UMM's generative ability to produce images for these scenes. Subsequently, an image-based question guessing and answering game is introduced by exploiting the understanding capability. STaR-Attack embeds the original malicious question among benign candidates, forcing the model to select and answer the most relevant one given the narrative context. Extensive experiments show that STaR-Attack consistently surpasses prior approaches, achieving up to 93.06% ASR on Gemini-2.0-Flash and surpasses the strongest prior baseline, FlipAttack. Our work uncovers a critical yet underdeveloped vulnerability and highlights the need for safety alignments in UMMs.