I wasn't able to make MahApps work with Caliburn's short syntax either.
However, the long syntax works for me:
<Controls:MetroTabControl DockPanel.Dock="Top"
Background="{x:Null}"
ItemsSource="{Binding Connections.View}"
SelectedItem="{Binding SelectedConnection}" Margin="10,0" >
<i:Interaction.Triggers>
<i:EventTrigger EventName="TabItemClosingEvent">
<cal:ActionMessage MethodName="CloseConnection">
<cal:Parameter Value="$source" />
<cal:Parameter Value="$eventArgs" />
</cal:ActionMessage>
</i:EventTrigger>
</i:Interaction.Triggers>
</Controls:MetroTabControl>