First, a nit-pick: Tunnelblick will never launch when your Mac starts up, but it will start when you log in (you may be logged in automatically after starting your Mac, of course, which can make it appear that Tunnelblick starts when the computer starts.)
When you log in, Tunnelblick should launch, if and only if:
- It was running when you last logged out (or shut down or restarted your computer, which log you out automatically before shutting down or restarting);
- A process with "openvpn" in its name is running; or
- A process with "tunnelblick-helper" in its name is running.
#1 is the usual situation. #2 and #3 happen only if you have one or more Tunnelblick configurations set up to "Connect when computer starts".
Note: from your question, the following doesn't appear to be your situation, but I want to mention it:
Not recommended, but if you have added Tunnelblick to your "Login Items" (in System Preferences : Users & Groups), it will launch when you log in because of that, and if any of #1,#2, or #2 are also true, it will cause Tunnelblick to launch a second time, which will cause Tunnelblick to display the "VPN Details" window.