ArcGIS supports a number of methods to georeference an image. IMHO its a matter of taste, what methods are associated with georeferencing, and what with "undoing" projection or distortion.
The simplest of them, the affine or 1st Order Polynomial supports translation, rotation, and scaling. This one is parameterized by the numbers saved in a "world file", the tfw file accompanying a tif for example.
All other methods, eg. 2nd and 3rd Order, need more (and other) parameters then this, saved in a world file. So when your tif files are georeferenced with one of these higher order methods, you cannot have a world file.
Since ArcGIS do not bake this info into the image, but supports it transparent to the user by maintaining these XML files, you get interoperability problems.
AFAIK QGIS/GDAL do not support this aux.xml stuff. Thus you only read the image, but not the georeference info.
A way to handle this situation is to run the rectify command in ArcGIS, which writes a permanently georeferenced image (and the world file). By thousands of files this is best done with a python script. Use the well sounding method
arcpy.Warp_management(), with empty source_pnt/target_pnt (or some dummy points as the image is already georeferenced) and algorithm