According to the Suspended user section of Description of various user states in Discourse, emails initiated by staff members are sent to suspended users. The purpose of this is to allow staff to have a channel of communication with suspended users.
I can see how being unaware of this bahaviour could lead to an awkward situation. Ideally, the admins on your site would have used whisper posts for your internal communication. Whispers posts do not create notifications for non-staff users.