While things like Extensions and Flags are set in one copy of the browser, and then synchronised with other copies accessed by your Google account, some of the changes made in Settings are 'local' to that copy of the browser' If you wish to alter the Setting in other copies then you need to do so manually.
Chrome notifications
Click here to read a 9to5Google article and learn how to turn off, or minimise, these prompts if they are annoying you.