Unity configured with PerRequestLifetimeManager() creating multiple instances of DbContext per request for WebApi requests, but not MVC requests

Here's my UnityConfig.cs:

public class UnityConfig
{
    private static Lazy<IUnityContainer> container = new Lazy<IUnityContainer>(() =>
    {
        var container = new UnityContainer();
        DependencyResolver.SetResolver(new UnityDependencyResolver(container));
        RegisterTypes(container);
        return container;
    });

    public static IUnityContainer GetConfiguredContainer()
    {
        return container.Value;
    }

    public static void RegisterTypes(IUnityContainer container)
    {
        container.RegisterType<IProjectContext, ProjectContext>(new PerRequestLifetimeManager());
    }
}

Here's my UnityWebApiActivator.cs:

public static class UnityWebApiActivator
{
    public static void Start()
    {
        Microsoft.Web.Infrastructure.DynamicModuleHelper.DynamicModuleUtility.RegisterModule(typeof(UnityPerRequestHttpModule));

        var container = UnityConfig.GetConfiguredContainer();
        var resolver = new Microsoft.Practices.Unity.WebApi.UnityDependencyResolver(container);
        GlobalConfiguration.Configuration.DependencyResolver = resolver;
    }

    public static void Shutdown()
    {
        var container = UnityConfig.GetConfiguredContainer();
        container.Dispose();
    }
}

Stepping through the code, I can see my container getting created with the appropriate registrations.

Here is a sample WebAPI controller:

[Authorize]
public class ProjectApiController : BaseApiController
{
    private readonly ProjectService _projectService;

    public ProjectApiController(ProjectService projectService)
    {
        _projectService = projectService;
    }

    [Route("api/project")]
    [AcceptVerbs("POST")]
    public HttpResponseMessage SendProject(ProjectDto projectDto)
    {
        return Request.CreateResponse(HttpStatusCode.OK, _projectService.SendProject(GetUsername(), projectDto));
    }
}

While my ProjectService constructor looks like this:

public class ProjectService : BaseService
{

    public readonly ProjectContext _db;
    public readonly NotificationService _notificationService;

    public ProjectService(ProjectContext db, NotificationService notificationService)
    {
        _db = db;
        _notificationService = notificationService;
    }
    // methods here
 }

Both MVC controllers and API controllers depend on ProjectService, yet WebAPI requests behave differently. When an MVC request is served, I get a single instance of ProjectContext created as desired. When a WebAPI request is served, every injection creates a new instance. This is not desired.

Why is this happening?

Update:

Per the below answer, I have changed

DependencyResolver.SetResolver(new UnityDependencyResolver(container));

to

DependencyResolver.SetResolver(new UnityHierarchicalDependencyResolver(container));

This resulted in:

The type Microsoft.Practices.Unity.WebApi.UnityHierarchicalDependencyResolver does not appear to implement Microsoft.Practices.ServiceLocation.IServiceLocator. Parameter name: commonServiceLocator

Which led me here, where the recommended solution leads to:

I currently have:

• Unity 4.0.1
• Unity.AspNet.WebApi 4.0.1
• Unity.Mvc 4.0.1
• Unity.MVC5 1.2.3

Upgrading packages is last-resort right now.