DirectAdmin and cPanel handles parked domains very differently, for directadmin they are simply domain pointers that you can not really alter any settings for (and thus not creating subdomains either technically).
The only way to rectify the mismatch in how they are handled would be to remove the domain from domain pointers and add it under domain management as a separate domain. Although this should not affect the files (it doesnt for pointers added through directadmins interface) you are adviced to make sure you have a copy of your site before making the changes as it has been noted by other user that it did in fact affect their files.
I'm gonna guess that you largely have promoted your own domain, so I'd recommend copying the files onto the folder that will be created when you add an domain and then set a redirect from the main one to your own domain in case it is used.