I've managed to surprise myself with some DNS configuration. This is the actual output of my terminal:
[]$ host www.sepa-converter.nl
www.sepa-converter.nl is an alias for sepa-converter.herokuapp.com.
sepa-converter.herokuapp.com has address 184.73.167.111
[]$ host sepa-converter.herokuapp.com
sepa-converter.herokuapp.com has address 184.72.248.52
The result is that if you browse to www.sepa-converter.nl, you do not get the content served by sepa-converter.herokuapp.com.
I've used sepa-converter.nl as an alias for overopsepa.nl. And I want the mails to keep showing up at my Google Apps account. For that reason I've kept the A and MX records, but just changed the CNAMES to point to another server.
Why doesn't this resolve www.sepa-converter.nl to the right heroku app?
UPDATE: I understand that heroku doesn't return the same IP each time and I understand that that's not a problem. The problem is that the http requests serve content that is coming from a different dyno than the one aliased. If you check www.sepa-converter.nl against sepa-converter.herokuapp.com you'll see a different index.html being served.
This hostname have more that one IP and it is not an issue. I got different IPs on each dig query made to this hostname:
Your DNS is properly configured, however the webserver you are referencing to is not configured to host the domain "www.sepa-converter.nl".
To make the webserver host "www.sepa-converter.nl" a "ServerAlias" must be configured in the apache configuration.
Reference ServerAlias in the apache documentation.
Nothing is wrong with your DNS setup. You need to tell Heroku about the hostname you want to use.