According to the website (https://vectordash.com/hosting/) they use a highly isolated Ubuntu image, so the person hosting the service shouldn't have access to the VM with your model or data on it. It would be nice if there was some third party audit of the software though, the models, the code, and even the training data can be pretty sensitive for researchers.
If your training data is sensitive, then Vectordash may not be the best GPU provider. But if you're a broke CS student like me who wants to participate in a few Kaggle competitions (after having burned up their AWS student credits in 3 days) without shelling out a bunch for a K80, then Vectordash might be pretty helpful!