React Iframe Smart Rerendering question

Made a base level react to ask how React handles maintaining the cursor position in iframes even though it's "rerendering" the DOM?

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/babel-core/5.8.24/browser.js"></script>
<script src="https://npmcdn.com/react@latest/dist/react-with-addons.js"></script>
<script src="https://npmcdn.com/react-dom@latest/dist/react-dom.js"></script>
<script src="https://facebook.github.io/react/js/jsfiddle-integration-babel.js"></script>

<div id="container">
</div>

JavaScript 1.7

var Hello = React.createClass({
  getInitialState: function() {
    return {newState: 0};
  },
  triggerUpdate: function() {
    console.log('trigger update');

    setInterval((function() {
      console.log('triggering update');
      this.setState({ newState: Math.random() });
    }).bind(this), 1000);
  },
  render: function() {
    console.log('rerender trigger');
    return (
      <div>
        <div onClick={this.triggerUpdate}>Trigger update</div>
        <iframe src="https://www.w3schools.com/TAgs/tryit.asp?filename=tryhtml_textarea" width="500" height="500"></iframe>
      </div>
    );
  }
});

ReactDOM.render(
  <Hello name="World" />,
  document.getElementById('container')
);