So far, Planner members got notifications about Planner Tasks assigments in their inboxes or as a conversation in the linked Office 365 Group. As part of the evolution in the integration between Teams and Planner, Tasks assignments in Planner are going to be notified in Teams in the following ways:
As conversations in a private chat between the user and the Planner Bot.
As a notification in the Planner Apps in Teams.
As a notification in the user’s activity feed in Teams.
From any of those locations, the user will be able to access and view the tasks assigned to him / her: