On-the-Fly Category Discovery (OCD) requires a model, trained on an offline support set, to recognize known classes while discovering new ones from an online streaming sequence. Existing methods focus heavily on offline training. They aim to learn discriminative representations on the support set so that novel classes can be separated at test time. However, their discovery mechanism at inference is typically reduced to a single threshold. We argue that this paradigm is fundamentally flawed as OCD is not a static classification problem, but a dynamic process. The model must continuously decide 1) whether a sample belongs to a known class, 2) matches an existing novel category, or 3) should initiate a new one. Moreover, prior methods treat the support set as fixed knowledge. They do not update their decision boundaries as new evidence arrives during inference. This leads to unstable and inconsistent category formation. Our experiments confirm these issues. With properly calibrated and adaptive thresholds, substantial improvements can be achieved, even without changing the representation. Motivated by this, we propose PACO, a support-set-calibrated, tree-structured online decision framework. The framework models inference as a sequence of hierarchical decisions, including known-class routing, birth-aware novel assignment, and attach-versus-create operations over a dynamic prototype memory. Furthermore, we simulate the proxy discovery process to initialize the thresholds during offline training to align with inference. Thresholds are continuously updated during inference using mature novel prototypes. Importantly, PACO requires no heavy training and no dataset-specific tuning. It can be directly integrated into existing OCD pipelines as an inference-time module. Extensive experiments show significant improvements over SOTA baselines across seven benchmarks.