The idea of extensions is that all/most of the usage “stays” inside the extension.
If you are sending people to your site to login and do other stuff, then you may be in violation as Twitch cannot “validate” the contents of the site meet with the guidelines, and an extensions sole purpose shouldn’t be to send people off site.
Borderlands extension only sends people offside to link their shift+twitch accounts and then sends them back to the extension, for example.
*My intrepration of the rules and guidelines here.