Recently, foundation models, particularly large language models (LLMs), have demonstrated an impressive ability to adapt to various tasks by fine-tuning large amounts of instruction data. Notably, federated foundation models emerge as a privacy preservation method to fine-tune models collaboratively under federated learning (FL) settings by leveraging many distributed datasets with non-IID data. To alleviate communication and computation overhead, parameter-efficient methods are introduced for efficiency, and some research adapted personalization methods to federated foundation models for better user preferences alignment. However, a critical gap in existing research is the neglect of test-time distribution shifts in real-world applications. Therefore, to bridge this gap, we propose a new setting, termed test-time personalization, which not only concentrates on the targeted local task but also extends to other tasks that exhibit test-time distribution shifts. To address challenges in this new setting, we explore a simple yet effective solution to learn a comprehensive foundation model. Specifically, a dual-personalizing adapter architecture (FedDPA) is proposed, comprising a global adapter and a local adapter for addressing test-time distribution shifts and personalization, respectively. Additionally, we introduce an instance-wise dynamic weighting mechanism to optimize the balance between the global and local adapters, enhancing overall performance. The effectiveness of the proposed method has been evaluated on benchmark datasets across different NLP tasks.