Try adding the onSuccess callback when you initialize the component in componentDidMount().
componentDidMount: function() {
gapi.signin2.render('g-signin2', {
'scope': 'https://www.googleapis.com/auth/plus.login',
'width': 200,
'height': 50,
'longtitle': true,
'theme': 'dark',
'onsuccess': this. onSignIn
});
},
...
Sources: https://developers.google.com/identity/sign-in/web/build-button, https://github.com/meta-meta/webapp-template/blob/6d3e9c86f5c274656ef799263c84a228bfbe1725/app/Application/signIn.jsx.