This is my understanding (It may be wrong as well).
Normalization is done to bring the data to the standard gaussian distribution N(0,1). When we use the trained model in dataset0 for transfer learning (to dataset1), we expect the data in dataset1 in N(0,1) as well. At this point, I would say, if the dataset1 is large enough, it is wise to use the mean and std of dataset1 to normalize the data in transfer learning. But mostly transfer learning is done for the datasets with considerably less data. Hence, the calculated statistics (mean and std) might not represent the dataset1 distribution. We could rather use the statistics (mean and std) from dataset0 for normalization in this case.
The practice of using the mean and std from dataset0 for normalization is prevalent while using ImageNet pre-trained models. As mentioned above, the statistics of ImageNet is calculated from 1 million natural images, which might hold for other datasets with natural images (with considerably less data) as well.