Team members can track and update task progress of their tasks in Tasks Page of Project Online. This helps project managers to get task updates quickly rather than they updating the task progress for each team member.
But … this comes with a cost. Each team member should be a user with Project Online license; at least Project Online Essentials license (check license cost here). Also selected resource categories such as generic, material will not be real users.
Assignment Owner field (introduced way back Project 2007) is here to rescue. This field is available for enterprise resources created in Project Online/Server. This field contains the name of the enterprise user who is responsible for entering status on a given assignment. By default, the default assignment owner is set to name of the resource being added/edited.
Schedules with generic resources or material resource or actual resource (who are either internal or external) without Project Online license can’t update the task status. In other words, we can’t ask generic resources representing role or material resources representing consumables or actual resources without license to update their task status.
The solution is to edit these resources in Resource Center and set enterprise resource with project online license (possibly a team lead) as their assignment owner.
Default assignment owner can be set in the Resource page, and you can change the assignment while assignment in Task Information page.