If you create a new project you will have to make that known to the cloud.
In general, what sync project does is to take the project from the cloud, remove your old tracks and import your new tracks and then puts it back. This counts for all members including the owner.
You cannot alter tracks of other members, but you can make copies and work on those or keep them for reference, as you created new tracks they are yours and can not be removed by anyone else. This way, every member is in control of their own tracks but cannot change other members’ tracks, but still can make copies (“read only” access).
As said, a new project is a seperate project and the cloud doesn’t know about it until you make it known there.
Hope that clarifies it.