You do not receive notifications about successful or unseccessful backups of Office 365 items, although backup notifications are enabled for your user. You do not see Office 365 backup results in 7-day history either.
Backup notifications for Office 365 are planned for the next version of Acronis Backup Cloud. Including Office 365 backup into 7-day history is planned for future versions.
Meanwhile you can configure operations dashboard and scheduled operations reports. These reports include the status of Office 365 backup activities and can be sent to your email.