This is my Procfile and it is working exactly as you describe:

release: python manage.py migrate
web: run-program waitress-serve --port=$PORT settings.wsgi:application

See Heroku docs on defining a release process:
https://devcenter.heroku.com/articles/release-phase#defining-a-release-command

The release command is run immediately after a release is created, but before the release is deployed to the app’s dyno formation. That means it will be run after an event that creates a new release:

• An app build
• A pipeline promotion
• A config var change
• A rollback
• A release via the platform API

The app dynos will not boot on a new release until the release command finishes successfully.

If the release command exits with a non-zero exit status, or if it’s shut down by the dyno manager, the release will be discarded and will not be deployed to the app’s formation.

Be aware, however, this feature is still in beta.

Update:

When you have migrations that remove models and content types, Django requires a confirmation in the console

The following content types are stale and need to be deleted:

…

Any objects related to these content types by a foreign key will also be deleted. Are you sure you want to delete these content types? If you’re unsure, answer ‘no’. Type ‘yes’ to continue, or ‘no’ to cancel:

The migrate command in your Procfile does not respond and the release command fails. In this scenario, remove the migrate line, push live, run the migrate command manually, then add it back for future deploys.