Having used React to build an app now, I'd like to share some thoughts to this question I asked half a year ago.
I recommend you to read
The first post is extremely helpful to understanding how you should structure your React app.
Flux answers the question why should you structure your React app this way (as opposed to how to structure it). React is only 50% of the system, and with Flux you get to see the whole picture and see how they constitute a coherent system.
Back to the question.
As for my first solution, it is totally OK to let the handler go the reverse direction, as the data is still going single-direction.
However, whether letting a handler trigger a setState in P can be right or wrong depending on your situation.
If the app is a simple Markdown converter, C1 being the raw input and C2 being the HTML output, it's OK to let C1 trigger a setState in P, but some might argue this is not the recommended way to do it.
However, if the app is a todo list, C1 being the input for creating a new todo, C2 the todo list in HTML, you probably want to handler to go two level up than P -- to the dispatcher, which let the store update the data store, which then send the data to P and populate the views. See that Flux article. Here is an example: Flux - TodoMVC
Generally, I prefer the way described in the todo list example. The less state you have in your app the better.