I am sorry, but I am not that good in this area, 

I found this under the menu tool style and change the border thickness to 1,1,1,1 but nothing changes. Is that the right property and right file? 

Line 1372 ,version 2018.1. 

Also which property has the color for mouseover? 

    <!-- JJD 12/4/07 - BR28873 -->
    <!-- Added Border style for menu item icon area background -->
    <Style x:Key="MenuItem_IconAreaBackground" TargetType="{x:Type Border}">
        <Setter Property="SnapsToDevicePixels" Value="True" />
        <Setter Property="Background" Value="{DynamicResource {x:Static igRibbon:RibbonBrushKeys.MenuToolPresenterLeftColumnFillKey}}" />
        <Setter Property="BorderBrush" Value="{DynamicResource {x:Static igRibbon:RibbonBrushKeys.GalleryItemGroupCaptionStrokeFillKey}}" />
        <Setter Property="BorderThickness" Value="1,1,1,1" />
    </Style>

<Window
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:prim="http://schemas.infragistics.com/xaml/primitives"
        xmlns:ig="http://schemas.infragistics.com/xaml"
        xmlns:igRibbon="http://infragistics.com/Ribbon" x:Class="WpfApplication1.MainWindow"
        Title="MainWindow" Height="350" Width="525">
    <Grid>
        <Grid.Resources>
            <SolidColorBrush x:Key="{x:Static igRibbon:RibbonBrushKeys.ButtonToolHoverCenterFillKey }"  Color="LightBlue"/>
            <SolidColorBrush x:Key="{x:Static igRibbon:RibbonBrushKeys.ButtonToolPressedCenterFillKey }"  Color="LightSkyBlue" />
            <SolidColorBrush x:Key="{x:Static igRibbon:RibbonBrushKeys.ButtonToolCheckedCenterFillKey }"  Color="LightSkyBlue" />


        </Grid.Resources>
        <StackPanel>
            <igRibbon:MenuTool  VerticalAlignment="Center" 
                            HorizontalAlignment="Center"
                            Caption="_Theme"
                            Loaded="MenuTool_Loaded"
                            Click="MenuTool_Click"
                            ButtonType="Segmented"
                            LargeImage="dog.jpg"
                            Width="100"
                            Height="25"
                            Margin="5"
                            BorderThickness="5"
                            >
                <igRibbon:ButtonTool    Caption="Blue"
                                    LargeImage="dog.jpg"
                                    igRibbon:MenuToolBase.MenuItemDescription="Menu item"/>
            </igRibbon:MenuTool>
            <Button Width="50" Height="25" Margin="5" Click="MenuTool_Click">Test</Button>
        </StackPanel>
    </Grid>
</Window>

private void MenuTool_Click(object sender, RoutedEventArgs e)
        {
            MessageBox.Show("Click");
        }

        private void MenuTool_Loaded(object sender, RoutedEventArgs e)
        {
            ItemsControl tmp = Utilities.GetDescendantFromType(sender as DependencyObject, typeof(ItemsControl), true) as ItemsControl;
            tmp.Background = Brushes.LightGray;

        }

Here is my code for the split button so far, I manage to find the part to change the on hover color and the background color for the menutoll.

But I couldn't manage to find how to make the border visible on initial state, and on mouse over color for the dropbox area. (You can see in the picture)

  How can I change these parameters ?