FWIW, TPoint corrects for atmospheric refraction at various target Altitudes.
I agree that when you are using Tpoint you are typically also using refraction correction, and I find it frankly confusing to know which software is doing what. None of the Tpoint model terms are for refraction. In TheSkyX, there is a refraction tab on the imaging system setup window, it's not part of Tpoint and TheSkyX can do refraction corrections without Tpoint. TheSkyX, AFAIK, manages the change to the current epoch (precession and nutation), time, and may or may not do refraction, depending on the mount (it always does refraction when calculating elevation). Tpoint manages all the mechanical pointing errors and the spatial orientation of the mount. In ASCOM and in TheSkyX's X2 interface, there's a parameter for each mount type called "NeedsRefraction," and if that is true, it means that the mount is just returning a mechanical position with no refraction correction, but when false it means that the mount has internal refraction correction active. Paramounts return this as true so that TheSkyX will "own" the refraction correction function, some Meade mounts return this as false because they do the refraction correction internally.
When you are in the 'Polar Alignment' Tab in Tpoint, there is a checkbox labeled "show alternative polar alignments." That then tells you how you can change ME (the polar alignment error term) to be the true pole, the refracted pole, or some variant between the two. At 45 degrees latitude, there's about an arc minute between the refracted and true pole. The recommendation in the report tells you which elevation setting will minimize which error and it also mentions that there are different optimal elevation settings to minimize wide angle field rotation depending on declination of your target.