Got my answer after contacting the Google Play Developer Support (Got their response faster than I expected). It seems that the primary e-mail of the developer account must be in the same domain as the Google Apps.
A quote from the response that I got from the Google Play Developer Support:
In order for the option to be available to restrict distribution to your domain, the primary email of the developer account must be part of that domain.
So adding a domain user as a user to the developer account will not work.
You might ask yourself the question "But how do I change my primary e-mail?". The answer to that question is that you can't. You need to make a new developer account, transfer your apps from the old one to the new one and after that (Although it is optional) request a cancellation and refund of the old account. More information about this can be found here: https://support.google.com/googleplay/android-developer/answer/139626?hl=en