Yes, you are doing something wrong. You can't put in NS1.(IP_ADDRESS). That doesn't make any sense and wouldn't work.
If you are going to host your own NS servers for a domain, you need to create a host record for NS1 and NS2 (or whatever name you want) with your registrar (ie: namecheap). You will tell them that NS1.DOMAIN.COM = the IP of your box. Repeat for NS2 with the other IP.
Then, for the authoritative NS servers for your domain, you would use ns1.domain.com and ns2.domain.com.
Yeah that's what I thought.
So I just did what you said, but do I have to change the DNS settings for ZPanel? Do I make ns1.domain.tld = main IP and ns2.domain.tld = other IP in ZPanel as well?