Not necessarily the answer to your issue but have you worked with any other feature class data...
Open a new data frame and set its coordinate system to WGS 1984 Web Mercator (Auxiliary Sphere) before adding any data.
Will the users features load into the data frame?
Is the transformation pop-up presented?
And does the Transformations... button give you any choices?
If that fails cancel out of adding the Feature class, and add features from the template data or from an Esri Data & Maps DVD.
Does that come in?
Does it prompt transformation?
Finally, try to add base map data from Bing Maps or ArcGIS Online service.
Does that go into the data frame without transformation?
Note: it should since that is the default coordinate system for Bing and ArcGIS Online services.
If only the original feature class source is faulting on insertion into the WGS 1984 Web Mercator (Auxiliary Sphere), then I'd suspect the extent of the data is not correctly set for the coordinate system it is set to.
p.s. Any suggestions, Melita K.?