If you want to use your Plesk server as the authoritative DNS server for your domains you need to:
1) Create nameserver host records (sometimes called something else, like "create nameservers" or just "host records") at your registrar, pointing ns1/ns2.your-nameserver-domain.tld to the IPs of your plesk box. Note that this is NOT the same as adding/editing DNS records. Not at all. It is done in a different place to adding/editing DNS records in most registrar control panels. This is the step you may have missed.
2) set your-nameserver-domain.tld to use the nameservers you just created
3) set a domain you wish to host on your plesk server to use these nameservers also
4) In the DNS records in Plesk for your-namserver-domain.tld, make sure you have NS records pointing ns1/ns2 to the same IPs (your plesk box) as you used in 1.
5) Change the DNS template in Plesk to add two NS records for each domain (and remove the default NS record) ns1.your-nameserver-domain.tld and ns2.your-nameserver-domain.tld. Any new domains will then have these namservers by default. And you can also tell Plesk to propagate these changes to existing domains you may have already added.
6) Make sure any domains you have already added to plesk have these two nameserver records.
OR
Instead of using your own nameservers and instead of using your Plesk box for authoritative DNS, just use your registrar's DNS servers, and configure the records as appropriate, with all the appropriate A records pointing to your plesk box.