Next Point-of-Interest (POI) recommendation plays a crucial role in location-based services by predicting users' future mobility patterns. Existing methods typically compute a single user representation from historical trajectories and use it to score all candidate POIs uniformly. However, this candidate-agnostic paradigm overlooks that the relevance of historical visits inherently depends on which candidate is being evaluated. In this paper, we propose CaST-POI, a candidate-conditioned spatiotemporal model for next POI recommendation. Our key insight is that the same user history should be interpreted differently when evaluating different candidate POIs. CaST-POI employs a candidate-conditioned sequence reader that uses candidates as queries to dynamically attend to user history. In addition, we introduce candidate-relative temporal and spatial biases to capture fine-grained mobility patterns based on the relationships between historical visits and each candidate POI. Extensive experiments on three benchmark datasets demonstrate that CaST-POI consistently outperforms state-of-the-art methods, yielding substantial improvements across multiple evaluation metrics, with particularly strong advantages under large candidate pools. Code is available at https://github.com/YuZhenyuLindy/CaST-POI.git.