After deeper investigations, I finally gave attention on DataTrigger.EnterActions and ExitActions. In my case, it was exactly that was needed to animate on both value of IsActvie property. This is a XAML-only solution (for brevity sake, I just put back the trigger part) :
<ControlTemplate.Triggers>
<DataTrigger Binding="{Binding IsActive}" Value="True">
<DataTrigger.EnterActions>
<BeginStoryboard>
<Storyboard>
<DoubleAnimation
Storyboard.TargetName="coloredRectangle"
Storyboard.TargetProperty="Width"
From="30.0"
To="250.0"
Duration="0:0:0.3" />
</Storyboard>
</BeginStoryboard>
</DataTrigger.EnterActions>
<DataTrigger.ExitActions>
<BeginStoryboard>
<Storyboard>
<DoubleAnimation
Storyboard.TargetName="coloredRectangle"
Storyboard.TargetProperty="Width"
From="250.0"
To="30.0"
Duration="0:0:0.3" />
</Storyboard>
</BeginStoryboard>
</DataTrigger.ExitActions>
</DataTrigger>
</ControlTemplate.Triggers>