I too am having issues with DNS resolution using ZCC 220.127.116.11 on macOS Catalina.
In my case, it looks like the DNS resolver gets changed by ZPA into a 100.64.0.1 address, and then is NOT restored to the normal IP addresses even once I log out of Zscaler.
Of course a 100.64.0.1 address is not reachable, and DNS fails.
Even by quitting completely the Zscaler Client Connector, the DNS remains stuck on 100.64.0.1, and only if I refresh the DNS configuration in the network control panel, the normal DNS servers are restored.
Check the status of your /etc/resolv.conf file and see for yourself if we are running into the same issue.
BTW, I use static DNS server configuration on my Mac, and not DHCP.
When I will open a case, I will update this message if there is anything relevant coming up.