During publish I selected Testing as configuration but it automatically change to "Release" after I click publish. And after publish completed it convert back to "Testing".
That is correct - it does revert to Release by default. I've raised an issue with this to get the acceptance of debug allowed in the experience and will push to try to get it back in there. FWIW, you can still debug a Web App with a WebJob in it if you enable remote debugging on the site.