Is storage related to the deployment model?
No, the location where the copies are stored is independent of where the management server is running - even with a SaaS deployment, you can store data locally and conversely - you can use any cloud storage with the management server deployed locally (On-Premise).
It is also worth adding that regardless of the deployment model, GitProtect.io will provide the same set of functionalities in exactly the same way via one graphical interface.