IIRC, SDC does not immediately clear cookies/cache on tab closing. It purges them on a scheduled interval. If you close the tab and wait a while (you should eventually see a toast message, if you have them enabled, saying something like "deleted x cookies from blah.com"), then your session should be removed. Closing the browser runs the purge immediately which is why that was working for you already.
Also, I had to close my browser for the test to be allowed to work (session expiry). I tried closing the tab, but that's not enough.
For me that is an unfair test as I hardly ever close my browser down completely.