Multimodal emotion analysis is shifting from static classification to generative reasoning. Beyond simple label prediction, robust affective reasoning must synthesize fine-grained signals such as facial micro-expressions and prosodic which shifts to decode the latent causality within complex social contexts. However, current Multimodal Large Language Models (MLLMs) face significant limitations in fine-grained perception, primarily due to data scarcity and insufficient cross-modal fusion. As a result, these models often exhibit unimodal dominance which leads to hallucinations in complex multimodal interactions, particularly when visual and acoustic cues are subtle, ambiguous, or even contradictory (e.g., in sarcastic scenery). To address this, we introduce SABER-LLM, a framework designed for robust multimodal reasoning. First, we construct SABER, a large-scale emotion reasoning dataset comprising 600K video clips, annotated with a novel six-dimensional schema that jointly captures audiovisual cues and causal logic. Second, we propose the structured evidence decomposition paradigm, which enforces a "perceive-then-reason" separation between evidence extraction and reasoning to alleviate unimodal dominance. The ability to perceive complex scenes is further reinforced by consistency-aware direct preference optimization, which explicitly encourages alignment among modalities under ambiguous or conflicting perceptual conditions. Experiments on EMER, EmoBench-M, and SABER-Test demonstrate that SABER-LLM significantly outperforms open-source baselines and achieves robustness competitive with closed-source models in decoding complex emotional dynamics. The dataset and model are available at https://github.com/zxzhao0/SABER-LLM.