Dance-to-music (D2M) generation aims to automatically compose music that is rhythmically and temporally aligned with dance movements. Existing methods typically rely on coarse rhythm embeddings, such as global motion features or binarized joint-based rhythm values, which discard fine-grained motion cues and result in weak rhythmic alignment. Moreover, temporal mismatches introduced by feature downsampling further hinder precise synchronization between dance and music. To address these problems, we propose \textbf{GACA-DiT}, a diffusion transformer-based framework with two novel modules for rhythmically consistent and temporally aligned music generation. First, a \textbf{genre-adaptive rhythm extraction} module combines multi-scale temporal wavelet analysis and spatial phase histograms with adaptive joint weighting to capture fine-grained, genre-specific rhythm patterns. Second, a \textbf{context-aware temporal alignment} module resolves temporal mismatches using learnable context queries to align music latents with relevant dance rhythm features. Extensive experiments on the AIST++ and TikTok datasets demonstrate that GACA-DiT outperforms state-of-the-art methods in both objective metrics and human evaluation. Project page: https://beria-moon.github.io/GACA-DiT/.