The access URL for the author tier should be:https://PROD/STAGING/DEVauthor-pNumber-eNumber.adobeaemcloud.com
It's far easier to understand which environment the URL relates too when viewed in a browser as people won't remember the p or e numbers. the same applies to the publish tier.
Please note that Cloud Manager allows you to add a custom domain to identify your site with a unique, branded name in a self-service manner via the UI. This is only supported for publish services and not supported on Author service.