When opening the ContextMenu and hovering over the first Item no Tooltip is displayed. Only when you move the mouse over another MenuItem on the same ContextMenu and then back to the first one the Tooltip gets displayed.
As a workaround, the telerik:RadToolTipService.ToolTipContent property can be used:
<telerik:RadMenuItem Header="I should display a tooltip" telerik:RadToolTipService.ToolTipContent="I am the tooltip that never shows" />
The template of the tooltip can also be modified to match the default tooltip style:
<Style TargetType="telerik:RadMenuItem" BasedOn="{StaticResource RadMenuItemStyle}">
<Setter Property="telerik:RadToolTipService.ToolTipContentTemplate">
<Setter.Value>
<DataTemplate>
<Border
Background="{telerik:FluentResource ResourceKey=PrimaryBackgroundBrush}"
BorderBrush="{telerik:FluentResource ResourceKey=BasicBrush}"
BorderThickness="1"
SnapsToDevicePixels="True">
<ContentPresenter Content="{Binding}" Margin="5"/>
</Border>
</DataTemplate>
</Setter.Value>
</Setter>
</Style>