An alarm clock is not self aware, because it doesn't model the world, and select between actions.
Similarly, a bee, (which I believe to act on pre-programed instinct, not in the moment reason), is not self aware. This is because it selects between actions, but can not logically model the world.
A dog, on the other hand, can build logical models of the world, and then take actions based on that. It can that begging from one person results in treats, while begging from another results in discipline. It can update this logic and behavior based on new information.