Explainable speech quality assessment requires moving beyond Mean Opinion Scores (MOS) to analyze underlying perceptual dimensions. To address this, we introduce a novel post-training method that tailors the foundational Audio Large Language Model for multidimensional reasoning, detection and classification of audio artifacts. First, a calibration stage aligns the model to predict predefined perceptual dimensions. Second, a reinforcement learning stage leverages Group Relative Policy Optimization (GRPO) with dimension-specific rewards to heavily enhance accuracy of descriptions and temporal localization of quality issues. With this approach we reach state-of-the-art results of 0.71 mean PCC score on the multidimensional QualiSpeech benchmark and 13% improvement in MOS prediction driven by RL-based reasoning. Furthermore, our fine-grained GRPO rewards substantially advance the model's ability to pinpoint and classify audio artifacts in time.