When a revision is created in Solution Manager, the revision consists of the vql statements to update the data sources, views, etc into the promotion environment. Configuration properties like the path for "core-site.xml" are only stored as a variable name, and the environment that the revision will be promoted to needs to have the updated path for core-site.xml plus any other configurations properties that are needed. The Validate tool in Solution Manager will flag any missing variables in the promotion environment and you can either port the current values or add a new ones in the "Create Missing VQL Properties" dialog.
But this is just for the path that the variable stores. Any changes to a file that the path points to are not saved by the revision, so those will need to be updated by another method.
So this is a long way of saying: if you want to use the same core-site.xml, just update the revision to use the current path. Either use the revision validation tool or Solution Manager will make it obvious for you to do this, as the revision will fail on promotion if that path does not exist. But, if you want to use a core-site.xml that's on a different server or has different values, you'll have to update that file in a separate method from Solution Manager and then ensure that the path variable in your promotion enviroment is correct.
Hope this helps!