1. Set an environment variable called CMDER_ROOT to your root Cmder folder (in my case C:\Program Files (x86)\Cmder). It seems to be important that this does not have quotes around it because they mess with concatenation in the init script.
2. In your WebStrom/IntelliJ/PhpStorm terminal settings, use "cmd" /k ""%CMDER_ROOT%\vendor\init.bat"" as the Shell path. The double-double-quotes are intentional, as they counteract the missing double quotes in the environment variable.
Note: Remember to restart the IDE. Otherwise, you won't see the difference.