Hi there, I have been trialing the AGOL Near Me widget with a non-web mercator basemap (New Zealand Transverse Mercator), and finding that the addresses returned when you click on the map are incorrect. It appears that it is taking the NZTM coordinates and assuming they are Web Mercator.
This is the result when clicking the NZTM map. Coordinates are: 1,743,724.0702, 5,919,606.5081:
This is the actual location of that address
This behaviour is not present if I use a web mercator basemap in AGOL.
That would be a bug then...
Also for an FYI...
according to the help it should use your own basemap coordinates Choose basemap—ArcGIS Online Help
check the sections on using your own basemaps and basemap considerations