I had an issues on Owner change functionality. I like to summarize them in this blog.
Before Dec CU, a resource must have 'Save project to Project server' permission to become an Owner for any project.
Afte this update, any resource can be a project owner and the resource no need to have save project permission to become an Owner. But this will work only if you try to update Owner field through UI (PWA site -> PDP page).
I mean to say if you try to change owner for a project through PSI and if the new owner does NOT have save project permission, you will get fault exception with Project Server related error (ProjectInvalidOwner). This issue was addressed in August CU.
To make this work with PSI, you have to install another hotfix/update - August CU .
Please follow Brian Smith blog for this update installation as it requires SharePoint also to be updated with latest patches.
NOTE - Owner is a project level field like other custom fields in Project Server. Project Server does not grant permissions to the new Owner on Owner change. It all depends on what permissions the new Owner has.