What version of Tunnelblick are you using, and what is the "Set DNS/WINS" setting that you are using?
Changes to do this on Yosemite were committed to the source code as
r3149 on Nov 18, 2014, so they are included in Tunnelblick 3.4.2 and 3.5beta02.
You must also use "Set nameserver" for the "Set DNS/WINS" setting. Other settings are not recommended and are included only for backward compatibility with old systems. They are not updated for new versions of OS X.
Output from the Tunnelblick 3.5beta02 log shows the following:
Flushed the DNS cache via dscacheutil
Will flush the DNS cache via discoveryutil udnsflushcaches...
Flushed the DNS cache via discoveryutil udnsflushcaches
Will flush the DNS cache via discoveryutil mdnsflushcache...
Flushed the DNS cache via discoveryutil mdnsflushcache
No matching processes were found
mDNSResponder not running. Not notifying it that the DNS cache was flushed
(The "No matching processes were found" message refers to a check for a process named "HandsOffDaemon". If "HandsOffDaemon" is running, mDNSResponder should **not** be notified that the cache was flushed because doing so causes "HandsOffDaemon" to crash the OpenVPN process.)