Digital Twin (DT) technology creates layered digital representations of physical system, asset or process, denoted as actual twin (AT). DT integrates heterogeneous data, models and semantic technologies, enabling monitoring, simulation, prediction, and optimization to enhance decision-making and efficiency, ensuring an accurate and dynamic representation of their physical equivalents. The rise of the internet of things (IoT) and cyber-physical systems (CPSs) has generated massive volumes of data, which require contextual information about their source and meaning to extract actionable insights. DTs address this need by unifying system data and behavior into coherent, multi-layered heterogeneous models. However, as real-world conditions and AT evolve, semantic drift emerges, leading to a progressive divergence between the DT and its AT, reducing reliability and effectiveness. Semantic drift often arises from inconsistent evolution and misalignment among heterogeneous models within the multi-layered paradigm, causing semantic mismatches, inconsistencies, and synchronization problems. Correcting semantic drift involves structural and behavioral adaptations across heterogeneous models and current methods typically involve manual updates, which are time-consuming, error-prone, and risk compromising data integrity. In this paper, we overcome these challenges and propose a systematic approach to manage semantic drift in multi-layered, model-driven DTs, supporting structural adaptation across heterogeneous models to ensure semantic consistency. We adopt a three-step approach: (i) identification, (ii) evaluation or measurement, and (iii) propagation, to manage semantic drift systematically. First, we identify and assess variants of semantic drift arising from data. We then propagate the changes across heterogeneous models to effectively correct semantic drift. Finally, we employ a case-based generalization strategy to illustrate our approach, showing how insights derived from specific use case support semantic drift management in broader contexts.