ItemsControl really just binds to a list and applies a datatemplate (border with background red) for each item in the list. As for the reason you're only seeing green, well there's probably nothing in the TabList property on your viewmodel. That way, nothing in the items template renders, and all you see is green.
You'll need to make sure that TabList is bound correctly (it exists on your datacontext, whether that's a view model or not) and that it has items in it.
Here's a simpler version of what you may want to accomplish:
<Grid x:Name="LayoutRoot" Background="Green">
<ItemsControl ItemsSource="{Binding Path=TabList, Mode=OneWay}">
<ItemsControl.ItemsPanel>
<ItemsPanelTemplate>
<StackPanel Orientation="Horizontal" />
</ItemsPanelTemplate>
</ItemsControl.ItemsPanel>
<ItemsControl.ItemTemplate>
<DataTemplate>
<Border Width="150" Background="red" Height="100" />
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
</Grid>