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The rise of big data distributed across heterogeneous and decentralised sources has driven the development of Federated Learning (FL), enabling collaborative model training without centralising sensitive information. Within this domain, Personalised Federated Learning (PFL) has emerged to address the challenge of adapting models to individual clients in decentralised environments where data distributions differ significantly across participants. While prior work has primarily focused on mitigating static statistical heterogeneity, the more dynamic and persistent problem of concept drift, where data distributions evolve over time, remains underexplored in PFL. Such temporal shifts can substantially reduce model accuracy in non-stationary environments, and impact real-world performance. Existing approaches tend to either optimise a single global model through aggregation or specialise models for individual clients, but none provide a unified mechanism that bridges the benefits of both strategies in the presence of evolving data, leaving a gap for a further robust and improved PFL solution. We propose PFL-DRIFT, a novel unified framework that introduces a two-level hierarchical aggregation paradigm to address both static and temporal distributional challenges. The framework integrates localised client-specific personalisation with adaptive global aggregation, supported by a lightweight selector module that dynamically identifies the most suitable strategy for the current environment. In addition, drift-aware normalisation is incorporated to mitigate degradation under evolving data distributions, strengthening stability in non-stationary settings. Extensive empirical experiments across diverse benchmarks demonstrate that PFL-DRIFT consistently outperforms state-of-the-art baselines. These results highlight the framework's robustness, adaptability, and practicality for large-scale federated deployments in dynamic big data environments.