I don't know how familiar are you with the whole DNS subject but assuming you know a bit the truth is that you have four options to get trough this and each one have it's own PROS and CONS.
A) Resolve the domains using Digital Ocean's DNS
This means for every new domain you add to the zPanel it also has to be defined on the Digital Oceans DNS.
PROS: You don't need to know much about zones and will be simple to handle.
CONS: If you are thinking on deploy a large network of websites this can be overwhelming because only the Digital Ocean's account owner will be able to manage the DNS in here and any new domain/sub-domain will need to have his intervention.
B) Resolve the domains using your zPanel's DNS
This means you need to define NS records pointing to your droplet IP address and set those NS on the domain registar.
PROS: Any user with an account on the zPanel will be able to add new domains/subdomains and your intervention won't be required since is not necessary to add this on the Digital Ocean's DNS
CONS: The name resolution will be handled by only one IP and this will generate some DNS alerts. Not critical at first if your but not recomendable for large deployments.
C) Resolve the main domain using the Digital Ocean's DNS and any aditional domains using the Droplet's DNS.
This means you need to have the NS records for your main domain glued to the Digital Ocean's DNS IPs and for the rest of domains you need to have those using your own NS glued to your droplet IP.
PROS: The main domain won't get any alert related to it's own name resolution and the only domain you will need to set on the Digital Ocean's DNS will be the main one and as before, any user with an account on the zPanel will be able to add new domains/subdomains and your intervention won't be required because those don't need to be named on the the Digital Ocean's DNS
CONS: Again, the name resolution will be handled by only one IP and this will generate some DNS alerts. Also a warning (not critical error) on the zones might report some NS as inconsistent if they are defined only on the child but not on the parent zone.
D) Use the domain registrar (for each domain) to organize the DNS zones. (If/When available, considering the domain resellers normally have not a clue about it and also that not all the registrars have and easy way to find this resource on their tools).
PROS: You don't have to worry about the Digital Ocean's DNS at all
CONS: Depends on your registrar tools how easy or difficult the process can be to manage the name resolution for the domain.
Depending on your choice there will be a few things to think about. Be aware that in the C option (The one I'm using) looks like there migth be a risk of conflict on the name resolution according to some people.
I'm currently counseling on the exactly same subject to another user here (FALUDEROCA) at Digital Ocean and I posted this on his behalf.
If you are jumping on this to manage a large webhosting activity you should start thinking about to have your own droplets for name resolution (NS1, NS2) with BINDS (at least two) and separate droplets for webserver and mail server in order to have a clustered scheme similar to this one.