Tasks you create or assign to yourself appear on the My Customers list. If the Customer also has an open Conversation with you and a Task, then the Task and the Customer appear separately on the list.
Tasks only appear in your My Customers list when they come from Inboxes you’re assigned to. Tasks you create but assign to other Agents or Inboxes — especially Inboxes you’re not assigned to — appear as updates in your Notifications Center.
Some Tasks may not immediately appear in your My Customer list, depending on how soon the Task is due. This is configured through the Task Routing Window setting. For example, if the routing window is set to seven days, you will not see Tasks appear in your list or route to you when you request more Tasks if the Task due date is more than seven days from being due.