I managed to solve it this way:
void payloadDataGrid_AutoGeneratingColumn(object sender, DataGridAutoGeneratingColumnEventArgs e)
{
string tooltip = null;
switch (e.Column.Header.ToString())
{
case "Column 1":
tooltip = "Tooltip 1";
break;
case "Column 2":
tooltip = "Tooltip 2";
break;
}
if (tooltip != null)
{
var style = new Style(typeof(DataGridCell));
style.Setters.Add(new Setter(ToolTipService.ToolTipProperty, tooltip));
e.Column.CellStyle = style;
}
}