The recommendation has been playing a key role in many industries, e.g., e-commerce, streaming media, social media, etc. Recently, a new recommendation scenario, called Trigger-Induced Recommendation (TIR), where users are able to explicitly express their instant interests via trigger items, is emerging as an essential role in many e-commerce platforms, e.g., Alibaba.com and Amazon. Without explicitly modeling the user's instant interest, traditional recommendation methods usually obtain sub-optimal results in TIR. Even though there are a few methods considering the trigger and target items simultaneously to solve this problem, they still haven't taken into account temporal information of user behaviors, the dynamic change of user instant interest when the user scrolls down and the interactions between the trigger and target items. To tackle these problems, we propose a novel method -- Deep Evolutional Instant Interest Network (DEI2N), for click-through rate prediction in TIR scenarios. Specifically, we design a User Instant Interest Modeling Layer to predict the dynamic change of the intensity of instant interest when the user scrolls down. Temporal information is utilized in user behavior modeling. Moreover, an Interaction Layer is introduced to learn better interactions between the trigger and target items. We evaluate our method on several offline and real-world industrial datasets. Experimental results show that our proposed DEI2N outperforms state-of-the-art baselines. In addition, online A/B testing demonstrates the superiority over the existing baseline in real-world production environments.