Prompt tuning, which adapts vision-language models by freezing model parameters and optimizing only the prompt, has proven effective for task-specific adaptations. The core challenge in prompt tuning is improving specialization for a specific task and generalization for unseen domains. However, frozen encoders often produce misaligned features, leading to confusion between classes and limiting specialization. To overcome this issue, we propose a confusion-aware loss (CoA-loss) that improves specialization by refining the decision boundaries between confusing classes. Additionally, we mathematically demonstrate that a mixture model can enhance generalization without compromising specialization. This is achieved using confidence-aware weights (CoA-weights), which adjust the weights of each prediction in the mixture model based on its confidence within the class domains. Extensive experiments show that CoCoA-Mix, a mixture model with CoA-loss and CoA-weights, outperforms state-of-the-art methods by enhancing specialization and generalization. Our code is publicly available at https://github.com/url-kaist/CoCoA-Mix.