From what I've gathered at the sessions and demos with the Cloud booth at Imagine 2016, you can use any tools and processes you want to use. If you already have processes implemented, they should not need to change (much).
The way the solution was presented was that you have a master git repo and within the web UI supplied by Platform.sh you create as many branches as you need. So you can have a branch for staging, and a branch for development. Then under those branches, you can have as many branches as you have features. It's a one-click deployment of a replica of the production system for your one feature. Each branch generates, at that time, a new environment which replicates the production environment.
So you do your code development after creating a branch within the new Platform.sh web UI and commit your code to that branch. Once it's passed your tests, you push up to the remote and your branch environment has the new code deployed to it (possibly through the web UI or done through git hooks). Each environment has a unique URL which you can then use to review that specific feature's changes.
The platform is proprietary; however, they have done as much as possible to make it as flexible as can be. The recipes used for creating deployments can be edited by you. There is also an easy way to add/remove environment variables for scripts so you can change the database credentials or sanitize all the data in the database if need be on each deployment.