Pass Xdebug cookie as part of the request (the one which is set by bookmarklet or browser extension, for example).
For this to work: make sure that "phone handle" icon is activated in advance in PhpStorm (Run | Start Listen for PHP Debug Connection).
P.S. If you are using Postman, Insominia or alike (another REST client) then the best / most transparent way IMO is to use Xdebug cookie. You're most likely already using separate Environments (e.g. "dev", "test", "production") so you can have such a cookie only where it is needed (depends on the tool and version used of course).
This way there is no need to edit the URL (even if you have it as a "conditional parameter" that is present for some environment and absent for another) or configure Xdebug to "debug all requests" at all.
An example of such Xdebug cookie from my Postman (edit it as needed; here it is set for the local some-domain.local.test fake domain):
XDEBUG_SESSION=value; Path=/; Domain=.some-domain.local.test; Expires=Tue, 19 Jan 2038 03:14:07 GMT;
Since the host URL should be a part of your Environment (e.g. the endpoint URL will be like \{\{host}}/api/v1/welcome) then such cookie will be sent to the dev domain only and not to the production one.
This was driving me crazy. I just updated to PHP 7.1 and xdebug that was working no longer worked. I updated the xdebug.so file (Linux) and php --version indicated that xdebug was indeed being loaded and working. But when I would use Postman the debugger never kicked on.
Here's the solution. If you are using Apache as your server then you need to enable the PHP 7.1 mods and reboot Apache: sudo service apache2 restart
PHPSTORM is my default filter string, you can use whatever you want. Your editor should be set up to filter connections by IDE key (filter string), and thats it. You should be able to debug the same way as from Chrome or FF.