If customers are using Backbone to synchronize data, they can specify to disable notifications for changes. This is possible with the advanced setting "sync.notifyUsers". However, this will not disable notifications for @-mentions of users.
Note: So far there is no option in Jira to disable these notifications. Please vote for JSWSERVER-19938 to make this happen.
One idea to avoid notifications: we could remove the @-mentions from the comment text, so that no email is sent out to the user(s).