Using separate nameservers for certain domain

I don’t want a site I’m making associated with the domain the nameserver are setup with so I added nameservers on the domain at Namecheap and in Virtualmin I added records for dns1 and dns2 and change both of my NS records to the new nameservers. Is there anything else I have to change? I see some stuff showing the old nameservers on the SOA record, do I need to change this at all or anything else?