It's wonderful that I'm able to refresh a Power BI dataset from SSMS's "Process Database" interface. The only issue is that the Power BI web interface doesn't show that the dataset is bring refreshe...
Thanks for your response, Robert.
I just refreshed a dataset using Microsoft.AnalysisServices.Tabular.dll (via Python), and the refresh history on the settings page still shows that the dataset was last refreshed yesterday. It seems like the PowerBI.com user interface isn't catching on to the fact that I've refresehed the data from the API.