Neural video compression (NVC) has demonstrated superior compression efficiency, yet effective rate control remains a significant challenge due to complex temporal dependencies. Existing rate control schemes typically leverage frame content to capture distortion interactions, overlooking inter-frame rate dependencies arising from shifts in per-frame coding parameters. This often leads to suboptimal bitrate allocation and cascading parameter decisions. To address this, we propose a reinforcement-learning (RL)-based rate control framework that formulates the task as a frame-by-frame sequential decision process. At each frame, an RL agent observes a spatiotemporal state and selects coding parameters to optimize a long-term reward that reflects rate-distortion (R-D) performance and bitrate adherence. Unlike prior methods, our approach jointly determines bitrate allocation and coding parameters in a single step, independent of group of pictures (GOP) structure. Extensive experiments across diverse NVC architectures show that our method reduces the average relative bitrate error to 1.20% and achieves up to 13.45% bitrate savings at typical GOP sizes, outperforming existing approaches. In addition, our framework demonstrates improved robustness to content variation and bandwidth fluctuations with lower coding overhead, making it highly suitable for practical deployment.