Accurate prediction of startup screw speeds in rubber weatherstrip co-extrusion is challenging due to batch-dependent process variation, material variability, and target-specific geometric constraints. This study proposes a hybrid fusion framework that integrates an autoregressive integrated moving average with exogenous variables (ARIMAX) model and a physics-guided feature-based artificial neural network (PG-ANN) to predict startup screw speeds for the Ø120, Ø90, and Ø70 extruders. The temporal model captures batch-to-batch process variations, while the PG-ANN uses input features constructed from material rheological properties and cross-sectional geometry. A process-change-driven branch-selection mechanism determines which model output is used for each production batch. The framework was evaluated using industrial co-extrusion data collected from a mass-production environment. In the hold-out test, the best-performing model differed across targets: ARIMAX showed the highest R² and lowest root mean square error (RMSE) for Ø120, the hybrid model achieved the best performance across all evaluated metrics for Ø90, and the PG-ANN performed best for Ø70. Model transferability was further assessed by applying the A1-trained framework to the A2 product condition without refitting; the Ø120 target showed poor transfer performance, consistent with the weaker batch-to-batch correlation observed in A2. The limited number of independent production batches and changes in batch-to-batch relationships across products constrain model generalization. The proposed framework provides a rule-based mechanism for selecting between complementary prediction branches using measurable process changes.