Unit testing async database methods

I have a Web API that I want to test using MS Test. I want to test one controller in particular. This is the init code:

public class MyControllerTests
{
    private static MyController controller;

    [AssemblyInitialize]
    public static void Initialize(TestContext context)
    {
        controller = new MyController();

        IoC.Register(Component.For<IDbContextFactory>().ImplementedBy<MockDbContextFactory>());
        // other config
    }
    // test methods, all async
}

This is the mock context factory. Is it used inside all the API methods to get a DB context.

public class MockDbContextFactory : IDbContextFactory
{
    MyContext context;

    public MyBaseContext GetContext()
    {
        if (context == null)
        {
            context = new MyContext(new DropCreateDatabaseAlways<MyContext>());

            //populate with mock data...
        }

        return context;
    }
}

Everything was nice until I added a test for the delete method. It is finished before the other methods, so it deletes objects from the shared context and the other tests fail. No I have two ideas: new context per method (using a [TestInitialize] resetter), but the underlying database is still the same and I get lots of key conflicts when inserting the new mock objects. Another idea is setting a new database in memory and having completely separate instances. I found Effort, but I believe this is an overkill and I'm approaching it wrong.

I am using Castle Windsor as the IoC container, in case there is a way to do it on the IoC level.