You are likely setting it on the Tab not the header. Try the header instead. This may require you to restyle the header.
You can restyle the header how ever you want though and then set the tooltip for the UI element you use to display the header.
Something like this should work.
Note: this was not tested so there may be errors in it.
<TabControl x:Name="tabCtrlMain" ItemsSource="{Binding Items}" >
<TabControl.Resources>
<Style TargetType="TabItem">
<Setter Property="Header" Value="{Binding FileName}" />
<Setter Property="HeaderTemplate">
<Setter.Value>
<DataTemplate DataType="{x:Type TabItem}">
<Border x:Name="grid">
<ContentPresenter>
<ContentPresenter.Content>
<TextBlock Text="{TemplateBinding Content}" Tooltip="{Binding Path=TooltInfo}"/>
</ContentPresenter.Content>
</ContentPresenter>
</Border>
</DataTemplate>
</Setter.Value>
</Setter>
</Style>
</TabControl.Resources>
</TabControl>
If you are directly adding tabs in XAML then just code right to the header.
i.e.
<TabItem>
<TabItem.Header>
<Grid>
<Grid.ToolTip>
</Grid.ToolTip>
</Grid>
</TabItem.Header>
</TabItem>