Large language models (LLMs) are now used worldwide, yet their multimodal understanding and reasoning often degrade outside Western, high-resource settings. We propose MMA-ASIA, a comprehensive framework to evaluate LLMs' cultural awareness with a focus on Asian contexts. MMA-ASIA centers on a human-curated, multilingual, and multimodally aligned multiple-choice benchmark covering 8 Asian countries and 10 languages, comprising 27,000 questions; over 79 percent require multi-step reasoning grounded in cultural context, moving beyond simple memorization. To our knowledge, this is the first dataset aligned at the input level across three modalities: text, image (visual question answering), and speech. This enables direct tests of cross-modal transfer. Building on this benchmark, we propose a five-dimensional evaluation protocol that measures: (i) cultural-awareness disparities across countries, (ii) cross-lingual consistency, (iii) cross-modal consistency, (iv) cultural knowledge generalization, and (v) grounding validity. To ensure rigorous assessment, a Cultural Awareness Grounding Validation Module detects "shortcut learning" by checking whether the requisite cultural knowledge supports correct answers. Finally, through comparative model analysis, attention tracing, and an innovative Vision-ablated Prefix Replay (VPR) method, we probe why models diverge across languages and modalities, offering actionable insights for building culturally reliable multimodal LLMs.