well, in most applications the buttons/paddles are connected to a normal manual gearbox with cogs and ratios not a torque converter like an automatic.
The button/paddle is like a button that cuts the throttle, disengages the clutch, changes gear, then reengages the clutch and throttle once the gear is selected. It is all an automated process and happens in a tenth of a second.
When i drove a Ferrari 360 with this paddle shift it was a strange experience, as you keep your foot planted on the throttle (or brake if downshifting for a corner) whilst changing gear, just as if you were playing Gran Turismo with a steering wheel or similar. The Ferrari 360 has a computer module that actually 'blipped' the throttle on down changes to provide smoother and quicker shifts.
This method of transmission is linked with throttles that are connected with fly-by-wire to the engine, rather than the conventional throttle cable used in most 'ordinary' cars.