Nowadays offline transfer learning (TL) is the mainstream research for cross-domain machinery fault diagnosis (MFD). However, the target data is usually collected online by edge devices in real-world applications, causing practicality issue of offline TL. To address this issue, a new and practical online TL scenario test-time adaptation (TTA) is considered in this paper. In TTA, the labeled source data is inaccessible for privacy, and only a pre-trained source model is provided for online model adaptation with the online unlabeled target data. To enable TTA for MFD, a dynamic data division strategy is proposed to divide each mini-batch of the online target data into the certain-aware and uncertain-aware sets based on the spectral entropy and prediction confidence for the subsequent fine-grained online model adaptation. Delving into underlying data properties, a customized contrastive learning (CL) framework is proposed, consisting of specifically designed CL strategies for the different divided sets, respectively. Specifically, prototypical CL based on the representative class-wise prototypes is proposed to boost the feature discriminability of certain-aware set, while neighborhood CL based on the local neighborhood structure is proposed to refine the numerous noise of uncertain-aware set. Meanwhile, smooth entropy minimization is devised for reliable model uncertainty reduction. The cloud-edge TTA implementation framework is further considered in the scenario of cloud manufacturing and edge computing for practical real-world applications. Specifically, the pre-trained source model is directly deployed from cloud to edge for local TTA. A simple source model pruning strategy is proposed to obtain the lightweight pre-trained source model for efficient deployment on resource-limited edge devices. Practical experiments on two edge devices Raspberry Pi and NVIDIA Jetson Nano verify the effectiveness and efficiency.