the DNS-Records are OK.
Tell me if I wrong to say that the co-domains must have two for each extension in the ISPConfig Co-Domains panel.
www.mywebsite.com <--- Main domain
mywebsite.net <--- this domain must be redirect the user to mywebsite.com and maintain the name of the domain .net in the url bar
What happens if the user type these following url?
Using these links, you will be routed under the primary domain?