I found that if WebTabItem object is added into TabPages before assign its PageTemplate, then the div and the text "This window is using...." is displayed.

protected void Page_Load(object sender, EventArgs e)
{
    WebTabItem myTabItem = new WebTabItem();
    myTabItem.Name = "Jim";
    myTabItem.Text = "Jim";
    myTabItem.ContentMode = ContentMode.UseInlineContent;
    WebTab1.TabPages.Add(myTabItem);

    String strContent = "<div class='text'>This window is using InlineContent mode created from code behind.</div>";
    myTabItem.PageTemplate = new GenericContainerTemplate(strContent);
    myTabItem.ToolTip = "Newly added TabItem";        
}

Hope this helps.