Multimodal Large Language Models (MLLMs) have significantly advanced the landscape of embodied AI, yet transitioning to synchronized bimanual coordination introduces formidable challenges in multi-stream multimodal integration. We introduce ST-BiBench, a comprehensive multi-tier framework for evaluating spatio-temporal multimodal coordination. Our approach centers on Strategic Coordination Planning, assessing high-level cross-modal reasoning over multiple action and perception streams. To investigate the "proximity paradox"-where semantically coherent plans fail to align with spatially grounded visual inputs-we incorporate Foundational Spatial Grounding to verify workspace awareness and arm-selection logic. Furthermore, we probe model frontiers through Fine-Grained Action Control, investigating whether MLLMs can directly synthesize high-dimensional continuous action modalities (16-Dim) from complex multimodal metadata. Evaluating 30+ state-of-the-art MLLMs, we uncover a persistent and pervasive "coordination paradox"-a significant gap between high-level strategic reasoning and fine-grained physical execution. Results reveal that while frontier MLLMs excel at logic-driven strategy, they frequently suffer from perception-logic disconnection and multi-stream interference during multimodal fusion. ST-BiBench provides a platform for identifying critical bottlenecks in multi-stream multimodal fusion and cross-modal alignment for complex embodied tasks.