For GS Mini, scoot the TWA just about level with the end of the guitar. It will lay flat, but due to the arch on the back, you may notice a gap of about 1/16" on the outer edges of the suction liners.
Attaching the TWA a bit south of the actual playing position and nudging it towards the neck will help to set the cone flat. I have no issues attaching to my GS mini.
The transducer cone is what vibrates to generate the effects. It doesn't have to be perfectly flat, but you want as much contact as you can get.
If your TWA is vibrating, then it's likely that the gain is too high or the X-brace isn't making a full connection (2 of 4 magnets making contact).