Please note: I have just started using AutoFac to learn about DI and IoC.
Is dependency injection supposed to be initialized in the controllers constructor?
Ho
Dependency Injection means exactly injection of dependency. It does not say anything about initialization. E.g. if you are injecting dependency which is Singleton, then it can be initialized long before you are injecting it.
Your first code is a usual dependency injection via constructor. Your second code is not dependency injection. Actually it looks odd to me - either you are trying to create instance of interface, which is not possible, or you have bad naming here. If it is just bad naming or typo, then second sample should really look like:
public IMyService iMyService = new MyServiceImplementation();
But you are not injecting anything here. You are simply creating dependency instance (which makes your controller coupled to dependency implementation).