I am testing my API in Postman and am having trouble simulating a log out.
If I do a call to delete the session cookie,
Have you tried Clear Cache extension? Give it a try. It clears app cache, downloads, file systems, form data, history, local storage, passwords and much more, available in the Options settings.
Update: try this answer https://superuser.com/a/232794
I'm not sure of a way to do this in Postman. I used to close the whole browser and reset the server in order to authenticate again. Never tested logout because it was an API service.