The built-in Hyperlink style is not applied to hyperlinks imported from HTML (<a> tag). As a result, the hyperlinks in the document do not have the blue underline.

Workaround: Subscribe for the SetupDocument event of the HtmlDataProvider and set the hyperlinks' style manually.
private void HtmlDataProvider_SetupDocument(object sender, Telerik.Windows.Documents.FormatProviders.SetupDocumentEventArgs e)
{
    StyleDefinition hyperLinkStyle = e.Document.StyleRepository[RadDocumentDefaultStyles.HyperlinkStyleName];
    hyperLinkStyle.SpanProperties.ForeColor = Colors.Green;//Color.FromRgb(0xff, 0x7a, 0xcc);
    var hyperlinks = e.Document.EnumerateChildrenOfType<HyperlinkRangeStart>();

    RadDocumentEditor editor = new RadDocumentEditor(e.Document);
    editor.Document.History.IsEnabled = false;

    foreach (HyperlinkRangeStart hyperlink in hyperlinks)
    {
        e.Document.Selection.SelectAnnotationRange(hyperlink);
        editor.ChangeStyleName(RadDocumentDefaultStyles.HyperlinkStyleName);
    }
    e.Document.Selection.Clear();

    editor.Document.History.IsEnabled = true;
}