When on a user’s profile, you can enable and disable various notifications settings for that user. This will affect what notifications are sent to Responders in that user’s Circle, either via SMS text message, or via an app-notification.
To do this, go to the "Info" menu button, and then scroll down the page, where you will find the “Event Settings” heading. Below this, there will be a list of all notification options available, with toggles to enable to disable them.