DNS leaks are a problem that have been encountered in other common VPNs, but with ZenMate enabled all DNS queries (the mechanism to connect domains to IPs) are routed through our network. The reason for this is to prevent DNS based hacking attempts, circumvent censorship using DNS poisoning and to speed up browsing as uncached DNS queries are often the slowest part of a HTTP request. On our servers we use a cached Google Public DNS which is one of the few DNS systems in the world without censorship.
It's important to note that our users do not connect to the Google DNS service directly but instead through the ZenMate network. As a result the Google DNS only sees the IP of the ZenMate network, not the user's IP address. When you run a test on dnsleaktest.com with ZenMate running, you'll see the Google DNS IPs listed, but your personal DNS is not leaked.
When using ZenMate for Opera you might need to make sure that this specific browser setting is enabled:
Go to Opera Settings / Preferences, scroll down to Network and check "Use proxy for local servers".