TemplateColumn: CellTemplateSelector seems not to work

[VisualAlf]

I've difficulties using the TemplateSelector in TemplateColumn.
A very simple project demonstrating is here: TemplateSelectorIssue.zip
It produces:

Note, that the column 'Selector-Column' is empty, but should have the same content as the 'String'-column (except that the third row should have the cell content in red).

I found the parameter (item) for the method:
protected override DataTemplate SelectTemplateCore(object item)
to always be null.

... or is there somewhat else ?