ReactJS: setTimeout() not working?

Do

setTimeout(
    function() {
        this.setState({ position: 1 });
    }
    .bind(this),
    3000
);

Otherwise, you are passing the result of setState to setTimeout.

You can also use ES6 arrow functions to avoid the use of this keyword:

setTimeout(
  () => this.setState({ position: 1 }), 
  3000
);