Multimodal Large Language Models (MLLMs) excel in Open-Vocabulary (OV) emotion recognition but often neglect fine-grained acoustic modeling. Existing methods typically use global audio encoders, failing to capture subtle, local temporal dynamics like micro-prosody and intonation shifts within individual utterances. To address this, we propose AcoustEmo, a time-sensitive MLLM featuring a novel Utterance-Aware Acoustic Q-Former. Our approach utilizes a timestamp-synchronized sliding window to dynamically extract segment-level audio tokens instead of coarse global representations. This enables the model to explicitly trace the temporal evolution of subtle acoustic clues and capture deep contextual dependencies in dialogues. Experiments on the Explainable Multimodal Emotion Recognition (EMER) task show that AcoustEmo significantly enhances complex emotion reasoning, outperforming baselines while maintaining robust contextual accuracy.