Productive currently does not support multiple assignees, but here's how you can work around that using Subtasks that can be assigned to multiple people.
Within a task, simply add as many subtasks as a task would have assignees and assign people to those subtasks.
In the example below, instead of having 2 assignees, I have created 2 subtasks with each having a different assignee.
Those subtasks will show up in their Tasks overview so they can always keep track of their work.
Also, note that you can leave the parent task's Assignee field blank. The only required fields on a task are its Title and Task list.
For smaller tasks, you can follow the same procedure and create To-do items instead of subtasks: