Do you have the options set to automatic for Forecast Model? If you can post both your Forecast Options window and the Describe Forcast - Summary & Models windows I can probably help you reconstruct it. You can definitely replicate this in R. You could also use ARIMA models in R if you want to try those as well (where you cannot in Tableau).
In the mean time, here are a couple resources about forecasting in Tableau:
https://www.interworks.com/blog/alentz/2014/09/22/data-forecasting-behind-voodoo (shameless plug for my blog)