To reproduce:
- Open the attached project. 
- Select the second tab and then the inner tabs.
- The layout is not updated.

Workaround:
private void TabStrip_ItemSelected(object sender, RadPageViewItemSelectedEventArgs e)
{
    LayoutControlTabStripElement el = sender as LayoutControlTabStripElement;
    foreach (LayoutControlTabStripItem  item in el.Items)
    {
        var groupItem = item.LayoutGroupItem;
        groupItem.Visibility = Telerik.WinControls.ElementVisibility.Visible;
        groupItem.InvalidateMeasure(true);
        groupItem.InvalidateArrange(true);
        groupItem.UpdateLayout();
        groupItem.Visibility = Telerik.WinControls.ElementVisibility.Collapsed;
    }

    foreach (LayoutControlTabStripItem item in el.Items)
    {
        if (item == e.SelectedItem)
        {
            var groupItem = item.LayoutGroupItem;
            groupItem.Visibility = Telerik.WinControls.ElementVisibility.Visible;
            break;
        }
    }
}

// access event
layoutControlTabbedGroup4.TabStrip.ItemSelected += TabStrip_ItemSelected;