This has nothing to do with DNS. It just means openvpn will also pull and apply network settings that contains names instead of only IP address or IP ranges. It is for setting up the VPN not for DNS queries after the VPN is set up.
Simply use the DNS server the VPN network tells you to use. The DNS server is usually send with the IP and other information to set up the VPN. If you want this automatically use NM or use a script that will do this. If you don’t want to use NM, a tool like resolveconf is usually required and need to be set up before it works.