You can edit the OpenVPN configuration files in Tunnelblick, see
Edit or Examine an OpenVPN Configuration File.
Tunnelblick is technically, an interface to OpenVPN, which is the program that creates and destroys an OpenVPN VPN.
DNS in OpenVPN, and thus in Tunnelblick, is manipulated in separate programs, usually called scripts (although they are technically just a command, which can run a script, a program, or execute a built-in command). See
Using Scripts.
Current versions of OpenVPN and Tunnelblick currently use "up" and "down" scripts, which are executed by OpenVPN when the VPN is established (up) and torn down (down). OpenVPN on macOS itself does not provide such scripts. Tunnelblick provides several sets of up/down scripts; users choose which one they want to use in Tunnelblick's "Set DNS/WINS" setting, or the VPN configuration can include custom up/down scripts.
OpenVPN 2.7, due soon, will introduce a new type of script to manipulate DNS, "dns-updown" scripts.