The ansible script that dashboard.literatecomputing.com uses runs a rake task after the new container is launched to do the post migrations. It counts on having SKIP_POST_DEPLOYMENT_MIGRATIONS turned on in the web_only.yml. I do this only on sites that I know will be managed by my scripts since if you don’t understand how it works if something of a time bomb.
Note that for many upgrades bootstrapping the new container won’t break things for the running container, but for some it does. It’s not that uncommon that an upgrade will migrate such that the old container can’t use the database (without using SKIP_POST_DEPLOYMENT_MIGRATIONS).