Questions about Tunnelblick are usually best asked on the Tunneblick Discussion Group. The Tunnelblick website is a good resource, too.
That said, it sounds like double-clicking the configuration file (.tblk, .ovpn, or .conf) isn't starting the correct copy of Tunnelblick. There are several system problems that can cause that, but it is easiest to just ignore them and force OS X to use the correct copy of Tunnelblick. If/when you have problems with other programs you can look into fixing whatever the underlying problem is.
Here's how you can get the configuration installed. (This assumes you have installed Tunnelblick. If not, please follow the instructions at Installing Tunnelblick.)
- Eject the Tunnelblick installer disk image if it is mounted.
- Open a FInder window, and locate "Tunnelblick" in Applications.
- Double-click Tunnelblick. Tunnelblick should launch and the Tunnelblick icon should appear near the Spotlight icon.
- Click on the Tunnelblick icon near the Spotlight icon, then click on "Quit Tunnelblick" in the menu that pops down. The Tunnelblick icon near the Spotlight icon should disappear.
- Drag and drop your configuration file(s) to the Tunnelblick icon in Applications in the Finder window.
- Tunnelblick should launch and ask how you want the configuration(s) installed.
If you have a question or problem at one of the steps, please detail which step and what the question or problem is.