Vision-Language Models (VLMs) extend Large Language Models (LLMs) with visual perception capabilities, unlocking broad applications across many domains. However, ensuring their safety remains a critical challenge, as adversarial visual inputs can easily bypass built-in safeguards and elicit harmful content. In this paper, we uncover a phenomenon we call delayed safety awareness, where a jailbroken VLM initially produces harmful content but ultimately recognizes the harmfulness at the end of the generation process. We attribute this phenomenon to the fact that the model's safety awareness against jailbreaks cannot be effectively transferred to the intermediate stages of text generation. Motivated by this insight, we introduce SafetyReminder, a simple yet effective defense that optimizes a learnable soft prompt using our proposed safety-activation prompt tuning. This soft prompt is inserted into the generated text to activate the safety awareness of the model, steering it toward refusal when harmful content arises while preserving helpfulness in benign scenarios. We evaluate our method on three established harmful benchmarks and across three types of adversarial attacks. Experimental results demonstrate that our method achieves state-of-the-art defense performance with strong generalization, offering a practical and lightweight solution for safer deployment of VLMs.