Recent Large Audio-Language Models (LALMs) have demonstrated promising abilities in understanding musical content. However, whether their responses are grounded in the correct temporal regions of the audio remains underexplored. This limitation is particularly critical for music understanding, where key information often occurs as temporally localized events, such as instrument entries and rhythmic transitions. To address this gap, we introduce MusTBENCH, a music-expert-validated benchmark designed to evaluate temporal grounding in LALMs through five temporally grounded question-answering tasks. To further improve temporal grounding in existing models, we propose MusT, a novel four-stage temporal optimization recipe spanning music encoder adaptation, LLM adaptation, LLM supervised fine-tuning, and RL-based optimization. Experiments on MusTBENCH show that existing LALMs struggle with precise temporal grounding, while MusT brings significant improvements over strong baselines. These results establish temporal grounding as a key missing capability in current LALMs and position MusTBENCH as a challenging benchmark for future research in temporally grounded music understanding.