That’s probably because when the Link is selected and SelectionAdorned is true, there is a selection handle object that is in front of the actual Link path. That’s the blue line you see that follows the link shape that you normally see when it’s not selected.
You just need to make sure the selection handle has the same tooltip.
Define that DataTemplate:
<DataTemplate x:Key="LinkSelectionAdornmentTemplate">
<Path go:NodePanel.Figure="None" Stroke="DodgerBlue" StrokeThickness="3" go:Part.Selectable="False" ToolTipService.ToolTip="My details of link" />
</DataTemplate>
And use it in your LinkTemplate:
<go:LinkPanel ... go:Part.SelectionAdornmentTemplate="{StaticResource LinkSelectionAdornmentTemplate}" ...>
Note that if you had indicated selection by modifying the appearance of your link, you wouldn’t have to customize the selection adornment template. That’s how the default link template works – it data-binds the path’s Stroke as follows:
Stroke="{Binding Path=Part.IsSelected, Converter={StaticResource SelectedLineBrushConverter}}"