The growing demand for personalized and private applications on devices highlights the importance of sourceless unsupervised domain adaptation (SFDA) methods, especially for time series data, where individual differences produce large domain shifts. As mobile devices with embedded sensors become ubiquitous, optimizing SFDA methods for parameter utilization and data sampling efficiency in time series contexts becomes crucial. Customization of time series is necessary to adapt to the unique patterns and behaviors of individual users, improving the relevance and accuracy of predictions. In this work, we introduce a novel paradigm for source model preparation and target-side adaptation aimed at improving the efficiency of both parameters and sample during the target-side adaptation process. Our approach re-parameterizes the source model weights with Tucker-style decomposed factors during the source model preparation phase. Then, at the time of adaptation of the target side, only a subset of these decomposed factors is adjusted. This strategy not only improves parameter efficiency but also implicitly regularizes the adaptation process by constraining the model capacity, which is essential for customization in diverse and dynamic time series environments. Furthermore, the proposed strategy achieves overall model compression and improves inference efficiency, making it very suitable for resource-constrained devices. Extensive experiments on several SFDA time series benchmark datasets demonstrate the effectiveness and efficiency of our approach, underscoring its potential to advance custom on-device time series applications.