Tagging data is saved in a database system that is saved somewhere it the ‘C:\users\%user%\AppData\Local\Google\Chrome\User Data\Default’ (in Windows) or ‘/home/%user%/.config/google-chrome/Default/IndexedDB/’ (in Linux) or ‘/Users/%user%/Library/Application Support/Google/Chrome/Default/IndexedDB/’ (in MacOS) route and is only legible for specific program.
So data is only accessible by the program for a specific user in a specific machine.
To use the data in other machine or by other Windows or Linux user, or to make backups of the data, the program has the option to export data to a file, and import it anywhere you need. Also databases are named and can be deleted by user with the program, so at a given time machine can be clean of the data used.