Within Teamwork, you can use board view triggers to automatically notify task assignees when a card is moved to a particular column.
Note: Board view triggers are available on paid Teamwork plans.
In the Board area of your project, click the options button (three dots) to the right of the column name and select Column Settings from the dropdown menu.
At the top of the column settings quick view panel, click the Add Trigger button in the Triggers section.
Choose Modify Properties as the trigger type in the Add Trigger modal. Once selected, you can then choose Notify Assignees from the second dropdown.
When the Notify Assignees trigger is added to a column, each time a card is then moved to that column, an email will be sent to the user(s) assigned to the task notifying them that the task has been edited.
For more information, see: Using Board View for Tasks