By default, 'Report User' will not send any emails to admin. However, it will create a new entry at your jomsocial backend -> reporting so that admin can take action on those reported users.

As for 'Report Group', it will only send an notification emails to site admin when the reporting threshold reached, which you can configure the reporting threshold at jomsocial backend -> global configuration -> site -> reportings and look for the option 'Execute default task when reach'.