Noted that you have already solved the problem.
The article seems to give two routes:
"With resolvconf, if you want entries to be present only when a particular interface is active, add a dns-nameservers line to the corresponding stanza in /etc/network/interfaces."
Which is what I think you have done.
"With resolvconf, if you want entries to be present all the time, add them to /etc/resolvconf/resolv.conf.d/head or /etc/resolvconf/resolv.conf.d/ tail, depending on whether you want them to be first or last."
I note that these files are not present. I think that all you need to do is create one or the other and they will be picked up.
I still don't quite understand why, if you are connecting to the same local router using either Ethernet or WiFi and using the router as your DHCP server in both cases, why you are not being given the same DNS Server configuration.
If it was a lack of name servers then you wouldn't be able to resolve anything - there should be nothing special about resolving the name of a time server as opposed to a web site or mail server.
It might be worth comparing the information in /etc/network/interfaces to see if there is something strange about your WiFi configuration as opposed to your Ethernet configuration.
Cheers
Dave R