Zenject factory from prefab not injecting into all components on prefab

I have a prefab "PlayerCharacterPrefab" with two components: PlayerCharacter and CharacterMovement. I am using zenject to bind a factory to produce PlayerCharacters from the "PlayerCharacterPrefab":

 Container.BindFactory<PlayerCharacter, Factory<PlayerCharacter>>().FromPrefab(_playerCharacterPrefab);

I have another MonoBehaviour that wants to create "PlayerCharacterPrefab"s at will. It looks something like this:

 public class PlayerCreator : MonoBehaviour
 {
     [Inject]
     private Factory<PlayerCharacter> _playerCharacterFactory;

     void Update()
     {
         _playerCharacterFactory.Create();
     }
 }

All of this works well, except for one problem. Both the CharacterMovement and PlayerCharacter components have dependencies which need to be injected. However, the factory is only injecting dependencies for the PlayerCharacter component when it instantiates the "PlayerCharacterPrefab".

My expectation is that the factory would inject dependencies for all components on the prefab. What am I doing wrong?