Once Requester Insights is turned on, go to Account > Job Launch Forms.
The ability to edit their requests is granted on a form-by-form basis. Click "Edit" for the each of the forms you'd like to grant access.
Then, check the box to "Allow submitter to edit Job Launch Request after submission" and click "Save Form."
Do this for all the forms you want requesters to be able to edit and you'll be all set! Just remember if you add new forms, you'll have to grant permission for those as well.
Here's a screenshot of the Edit button your requester will see on their dashboard: