When we look at the GeoTIFF keys it seems that ArcGIS would use latitude of true scale as origin which it actually does not do since the projected coordinate values are not 0 at that latitude. In other words ArcGIS writes Mercator (2SP) parameters in GeoTIFF's Mercator (1SP) fields. That causes major misalignment in softwares which interpret the GeoTIFF headers following the specification. My data ends up in latitude around 75.