I'm sorry you're having this problem. It is very weird, but there is a simple explanation.
You get that dialog if you have Tunnelblick 3.5.0 installed, and you double-click on a copy of Tunnelblick 3.4.0 that is not located in /Applications. The clue is that the dialog says "must be installed in Applications".
You may think you are double-clicking on an alias or shortcut to Tunnelblick, but you aren't -- you are double-clicking on a copy of Tunnelblick 3.4.0.
Or, if you are single-clicking on an icon in the Dock, it is not a link to the Tunnelblick in /Applications, but rather is a link to Tunnelblick 3.4.0 somewhere else.
Or you are double-clicking the Tunnelblick icon in a Tunnelblick 3.4.0 disk image.
Here is how you fix this: once Tunnelblick 3.5.0 is installed, drag whatever you are double-clicking on to the Trash or drag the Tunnelblick icon out of the Dock, as the case may be. You can then drag the Tunnelblick icon from /Applications to wherever you want – the Desktop, the Dock, or wherever – which will create an alias, and then use that alias to launch Tunnelblick.
(By the way, most people just leave Tunnelblick running all the time (but not necessarily connected to a VPN). It doesn't use many system resources if it is running but not connecting to a VPN. If Tunnelblick is running when you log out, or restart or shut down your computer, it will automatically be launched when you next log in.)