you should solder the spring to the driver, yes. It needs to have a stable connection. The driver touching the edge of the host shouldnt matter, because if you look in the host you can see that theres a sort of sleeve that comes partway up, and goes all the way down to the tailcap- where this "sleeve" makes a little ledge is where the spring (soldered to the outside ring on the driver) should sit, making contact with the batteries negative output (current travels up that sleeve, through the spring, to the driver). So actually even if the rest of the host IS conductive, it will be conductive from the negative side of the battery-- and the only thing that could touch the side is the outside ring of the driver, which if you recall, is the negative in.
So that being said, i have no idea whats causing yours to have problems :/ I might go put together another one real quick and see if i run into any problems