The TW7ToolButton does not appear to have an event for clicking on the split button arrow so this may be the best you can do with the current component version:
procedure TForm1.W7ToolButton1Click(Sender: TObject);
var
iPoint: TPoint;
begin
iPoint := ClientToScreen(Point(W7ToolButton1.Left, W7ToolButton1.Top + W7ToolButton1.Height));
PopupMenu1.Popup(iPoint.X, iPoint.Y);
end;
The menu will appear under the button just like a dropdown menu.