$access_tokens doesn't contain an index oauth_token_secret

You’re mixing up the APIs. JTV uses OAuth version 1, while Twitch uses version 2. So you shouldn’t be using the JTV guide to integrate with Twitch.

OAuth version 2 basically does away with all the signatures and different tokens, so you’ll just get one token straight up, which you’ll provide over HTTPS.

Read the Twitch authentication guide here: https://github.com/justintv/Twitch-API/blob/master/authentication.md