The fastest way to see who ticked an instance off in an Activated Checklist is to simply hover your mouse cursor over the checked box. When you hover over the instance, an information box will appear that shows the time and date that the box was ticked, as well as the full name of the user that checked the instance off the list.
For more information on who has used your Activated Checklists, you can also view the full Checklist Instance Report in the Reports section of your Way We Do manual.