Anyone who encounters this with Alertify 0.4.0 (currently RC1) can solve this by reseting the Alertify elements you're using. In my case, it was Alertify.dialog:
Alertify.dialog.el = false
// Do your normal JS stuff
In my crude understanding of this, Alertify thinks that a dialog element has been created, but when Turbolinks loads a page, it destroys that element. We need to tell Alertify it has been destroyed and Alertify will recreate it.
If you need any help with specifics, let me know.