The role of reasoning in Audio Large Language Models remains widely underexplored, as introducing a reasoning process often degrades rather than improves performance during inference, a phenomenon we term test-time inverse scaling, where longer reasoning chains yield progressively worse results. We demonstrate that this stems not from fundamental limitations of reasoning itself, but from inadequate training: models without proper guidance for the reasoning process produce hallucinatory, inconsistent reasoning that accumulates errors over longer chains. To address these challenges, we introduce CESAR (Consistent, Effective, and Scalable Audio Reasoners), shifting from outcome verification to rewarding the reasoning process. Our online reinforcement learning framework employs Group Relative Policy Optimization with a multi-faceted reward suite that incentivizes not only correctness and format but also consistency, structured analytical patterns, causal reasoning, domain-knowledge integration, and calibrated reasoning depth. CESAR resolves test-time inverse scaling, transforming reasoning from detriments into gains while revealing model-specific ``reasoning sweet spots", where performance peaks during test-time scaling. We achieve state-of-the-art results on MMAU Test-mini, substantially outperforming Gemini 2.5 Pro and GPT-4o Audio, and near-human-level performance on MMSU reasoning tasks. Through AI-as-judge evaluations and qualitative comparisons, we provide both quantitative and qualitative validation of our improved reasoning quality. Importantly, enhanced reasoning creates synergistic effects, simultaneously improving multimodal reasoning and perception capabilities. Overall, CESAR establishes a principled method for developing robust and scalable reasoning in Audio LLMs.