Probably you’d figured this out by now? But this may help somebody else as… I was in a similar position thinking that as well and trying to “enable” logging for nsd.
NSD is not very chatty but it logs in to the syslog:
deploy@box:~sudo grep nsd /var/log/syslog*
/var/log/syslog:Feb 12 16:26:29 box nsd: SIGHUP received, reloading...
Also if you have enabled secondary NS “slaves” ( or allow transfers,test check xfr:IP) under:
https://box.example.com/admin > System > CustomDNS > Using a secondary nameserver > Hostname
You should see any failed or successful transfers to the slaves if any zone changes occur.
However, It does not seem to log if I add my router external IP - xfr:IP and use dig to test:
dig axfr @ns1.box.example.com example.com from behind my router.
I can get full zone details from NSD for example.com but this is not logged in syslog.