Which option is more "authentic"? Or do we have both flavors available in the wild?
If you have at least 3 components dedicated to model, view, and controller, respectively, you're authentically MVC. How those components communicate isn't standardized. Why? Because MVC is our oldest design pattern. It was created before we had any idea how communication should happen between those components. Therefore the focus of the pattern is about separating these concerns.
This is why if you do a google image search for Model View Controller you don't see consistency in the arrows of the diagrams. You see stuff like this:
So if you've had trouble figuring out the "authentic" way to wire up the 3 components you're in good company. The MVC pattern simply doesn't tell us how to do this.
But, there are other patterns that do:
Those patterns talk about how to communicate. But every one can be thought of as following MVC. So if you just tell me you're using MVC please don't think you've told me how your components communicate. I'd have no idea. That's not part of the pattern.
Now that said, there is something called the principle of least astonishment. Your first option doesn't make me bat an eye. But your second? Well, if you told me your Controller was observing the Model my reaction would be, "Huh, ok, why?"