This paper describes the architecture of our system developed for participation in Task 3 of SemEval-2024: Multimodal Emotion-Cause Analysis in Conversations. Our project targets the challenges of subtask 2, dedicated to Multimodal Emotion-Cause Pair Extraction with Emotion Category (MECPE-Cat), and constructs a dual-component system tailored to the unique challenges of this task. We divide the task into two subtasks: emotion recognition in conversation (ERC) and emotion-cause pair extraction (ECPE). To address these subtasks, we capitalize on the abilities of Large Language Models (LLMs), which have consistently demonstrated state-of-the-art performance across various natural language processing tasks and domains. Most importantly, we design an approach of emotion-cause-aware instruction-tuning for LLMs, to enhance the perception of the emotions with their corresponding causal rationales. Our method enables us to adeptly navigate the complexities of MECPE-Cat, achieving an average 34.71% F1 score of the task, and securing the 2nd rank on the leaderboard. The code and metadata to reproduce our experiments are all made publicly available.