You should explicitly/manually set the Redirect URI in the Twitch.init call:
<script src="https://ttv-api.s3.amazonaws.com/twitch.min.js"></script>
<script>
Twitch.init({
clientId: 'YOUR_CLIENT_ID_HERE',
redirect_uri: 'http://www.mydomain.com'
}, function(error, status) {
// the sdk is now loaded
});
</script>
Of course be way about if your Twitch Application has a / on the end of the callback URL or not and update redirect_uri accordingly (for a while I was stumped as safari was being an ass and autocompleting the field with a / on the end)