Industrial workflows demand adaptive and trustworthy assistance that can operate under limited computing, connectivity, and strict privacy constraints. In this work, we present MICA (Multi-Agent Industrial Coordination Assistant), a perception-grounded and speech-interactive system that delivers real-time guidance for assembly, troubleshooting, part queries, and maintenance. MICA coordinates five role-specialized language agents, audited by a safety checker, to ensure accurate and compliant support. To achieve robust step understanding, we introduce Adaptive Step Fusion (ASF), which dynamically blends expert reasoning with online adaptation from natural speech feedback. Furthermore, we establish a new multi-agent coordination benchmark across representative task categories and propose evaluation metrics tailored to industrial assistance, enabling systematic comparison of different coordination topologies. Our experiments demonstrate that MICA consistently improves task success, reliability, and responsiveness over baseline structures, while remaining deployable on practical offline hardware. Together, these contributions highlight MICA as a step toward deployable, privacy-preserving multi-agent assistants for dynamic factory environments. The source code will be made publicly available at https://github.com/Kratos-Wen/MICA.