How do I turn off Local Snapshots for Time Machine?

Open the Terminal in the Utilities folder and enter or paste the appropriate command line. Press RETURN and enter your admin password when prompted. It will not be echoed.

To turn them ON: sudo tmutil enablelocal

To turn them OFF: sudo tmutil disablelocal

Note that turning them OFF will also delete all existing snapshots.

And that would take effect syste-wide or only the for current user account the commande was performed into?

Thanks.

Only for the logged in account in which they were created. Time Machine creates separate backups for different users even on the same computer.