How do assignments work?
When connecting a shared inbox in Slack or Teams, each Email, Facebook or Twitter conversation has an Assignee (i.e a person in charge of the conversation).
New conversations arrive unassigned: as long as they remain unassigned, reminders to reply or take action are posted in the channel. Once they have been assigned, reminders are posted in a private DM/chat to the assignee.
You can define a Default Assignee from the Settings page.