I'm sorry, I didn't use external nameservers for so long that I'm not 100% sure anymore.
As far as I remember (if I remember correctly) in the admin configuration section itself, it should still read ns1.hostingcompany.com and ns2.hostingcompany.com.
If you are logged in as admin and choose reseller level, then you can use the "set the name servers that will be assigned to new users" there and point to the acx.nl nameservers. I think you did that so that seems correct.
And then in the customer domain section in DNS it should read in Directadmin:
ns1.hostingcompany.com 3600 NS nszero1.axc.nl.
ns2.hostingcompany.com 3600 NS nszero2.axc.nl.
(mind the trailing dot).
If I'm not mistaken... it's a long time ago I worked with external nameservers so I'm doing this out of my head.
I've just checked the changes you made with the axc nameservers and it seems it's correct now.
Check the ip in DNS of the customer which is used. This should all be your vps ip's.
Also check /etc/virtual/domains if the domain is present in that file.
Same for /etc/virtual/domainowners if the domain and the accountname is in there.
Also check the help file.