The current tools we have for managing code only allow us to push code to the whole subscription (a Drupal docroot) at a time. Since each docroot contains code for many sites, it is necessary that we be able to push code at any time. So you need to only have code in the git repositories / branches that you have provided us as your source code (for dev, stage, and production) that can be pushed to your site.
When you are ready to push code from your repo, place the code in the correct branch and send a request to firstname.lastname@example.org.
We are working with the vendor to identify ways to allow you to manage pushing your code without opening a support request and without pushing the code for other sites on your subscription.