Span-level emotion-cause-category triplet extraction represents a novel and complex challenge within emotion cause analysis. This task involves identifying emotion spans, cause spans, and their associated emotion categories within the text to form structured triplets. While prior research has predominantly concentrated on clause-level emotion-cause pair extraction and span-level emotion-cause detection, these methods often confront challenges originating from redundant information retrieval and difficulty in accurately determining emotion categories, particularly when emotions are expressed implicitly or ambiguously. To overcome these challenges, this study explores a fine-grained approach to span-level emotion-cause-category triplet extraction and introduces an innovative framework that leverages instruction tuning and data augmentation techniques based on large language models. The proposed method employs task-specific triplet extraction instructions and utilizes low-rank adaptation to fine-tune large language models, eliminating the necessity for intricate task-specific architectures. Furthermore, a prompt-based data augmentation strategy is developed to address data scarcity by guiding large language models in generating high-quality synthetic training data. Extensive experimental evaluations demonstrate that the proposed approach significantly outperforms existing baseline methods, achieving at least a 12.8% improvement in span-level emotion-cause-category triplet extraction metrics. The results demonstrate the method's effectiveness and robustness, offering a promising avenue for advancing research in emotion cause analysis. The source code is available at https://github.com/zxgnlp/InstruDa-LLM.