I have some real technical issues with these statements.....I'm not sure if you can change your approach, but here are some thoughts....
Identification of differencing orders is being done on the premise that 1) there are no pulses, level shifts, seasonal pulses and/or local time trends AND that one model is adequate for the entire time range (constancy of parameters assumption) AND that the variance of the error process is homogeneous (constancy of variance assumption) And that the underlying ARIMA process is white noise. For example a series that has a level shift will exhibit an ACF that suggests non-stationarity BUT the remedy is not to difference.
You say "The Microsoft Time Series algorithm works by taking values in a data series and attempting to fit the data to a pattern. If the data series is are not already stationary, the algorithm applies an order of difference. Each increase in the order of difference tends to make the time series more stationary."
I think this is not robust enough. Over-differencing can induce non-stationarity se the Slutzky effect en.wikipedia.org/.../Slutsky_equation
In general, Over-differencing yields non-invertible MA structure often suggesting equation simplification is in order.