As you have noticed, when dealing with Custom Controls you'll often need to do some custom styling to reconfigure the layout. It all depends how far you want to take it, but to give you an idea I believe the workflow below should fix the backgroundcolor.
The backgroundcolor is bound to Xceed's resource themes, snippet from Wpf Toolkit:
<Style x:Key="NumericUpDown" TargetType="{x:Type prim:InputBase}">
<Setter Property="Foreground" Value="{DynamicResource {x:Static SystemColors.WindowTextBrushKey}}" />
<Setter Property="Background" Value="{DynamicResource {x:Static themes:ResourceKeys.ControlNormalBackgroundKey}}" />
<Setter Property="BorderBrush" Value="{DynamicResource {x:Static themes:ResourceKeys.ControlNormalBorderKey}}" />
</Style>
The ModernUI Style (following the chosen theme) for these properties folows e.g. ModernUI TextBox:
<Style TargetType="{x:Type TextBoxBase}">
<Setter Property="Foreground" Value="{DynamicResource InputText}"/>
<Setter Property="Background" Value="{DynamicResource InputBackground}"/>
<Setter Property="BorderBrush" Value="{DynamicResource InputBorder}"/>
</Style>
The DynamicResources are found in the theme file, for example ModernUI.Dark.xaml
<SolidColorBrush x:Key="InputText" Color="#d1d1d1" />
<SolidColorBrush x:Key="InputBackground" Color="#333333" />
<SolidColorBrush x:Key="InputBackgroundHover" Color="#3e3e42" />
<SolidColorBrush x:Key="InputBorder" Color="#333333" />
You can now hard code them in your Style, making them fixed on 1 theme
<Style TargetType="{x:Type local:IntegerUpDown}">
<Setter Property="Foreground" Value="#d1d1d1" />
<Setter Property="Background" Value="#333333" />
<Setter Property="BorderBrush" Value="#333333" />
</Style>
For extensive styling you'll need to put in more work, for example this post
adresses restyling the Watermark property.