Description
You are using the ArcGIS Online/Google Maps/Bing Maps tiling scheme and there is no datum transformation from your data source's datum to WGS 1984 Major Auxiliary Sphere. WGS 1984 Major Auxiliary Sphere is the datum for the WGS 1984 Web Mercator (Auxiliary Sphere) coordinate system used by the ArcGIS Online/Google Maps/Bing Maps tiling scheme. Tiles cannot be created accurately without a proper datum transformation.
Solution
Choose a tiling scheme that uses the same coordinate system as your data source.
Create an appropriate custom transformation using the Create Custom Geographic Transformation tool from your data source's spatial reference's geographic coordinate system to the geographic coordinate system for the ArcGIS Online/Google Maps/Bing Maps tiling scheme, which is WGS 1984 Major Auxiliary Sphere.