Transfer learning （TL） enhances remaining useful life (RUL) predictions by addressing data scarcity and operational challenges. Nonetheless, when a significant disparity in degradation data distribution exists between source and target domains, single-source domain TL may lead to misleading or negative transfer. Multisource domain TL partially mitigates these issues but fails to account for substantial discrepancies in feature-label correlations, impairing RUL prediction accuracy. To cope with this problem, we propose a multisource domain unsupervised adaptive learning method powered by a temporal convolutional network. Using a multilinear conditioning strategy, we combine degradation data and subregion labels to construct input characteristics for the domain discriminator. Additionally, we design a feature extractor that produces label-related features invariant across domains, thereby enhancing prediction precision. We evaluate our method using the publicly available C-MAPSS degradation dataset, demonstrating its effectiveness through a case study and ablation experiments.