Can you show us a bit more of your domain model? It sounds like task lists are not currently unique to each employee, so they are all editing the same list. You'll want to make sure that both the TaskItems and Checklist are separate objects for each of them. Alternatively, if the possible taskitems for everyone are the same, you might want to create an entity in between the Taskitems and the Checklist so you can assign them to people.
This is my domain model. I am assigning an Employee with a Checklist. Each task Checklist will have many different Taskitem and are taken from the Taskitems table. I tried to create an entity between the Checklist and the Taskitems, which has the Status and Remark properties. But when using listview to display, other properties can be edited, only the status and remark properties are not editable.