How to properly dockerize Ember.js FastBoot

Deploying a dockerized Ember.js app stack can be done with three or four containers. For https it's easiest to proxy over a specialized container that handles vhosts and ssl certificates.

              Internet
                 │
               Server
                 │
             Container
            nginx-proxy
               https
                 │
         ╭───────┴───────╮
    Container        Container
      Ember             API
www.example.com   api.example.com
                         │
                     Container
                         DB

This works fine. But when the Ember app becomes a FastBoot app, the FastBoot server will do the requests to the API for the first pageview server-side. And the API is not reachable via DNS, nor is it https.

How should a setup like this realistically be accomplished?