You should only support/jack the underside of the car at these 4 locations otherwise you will damage the battery.
The jack pads (hockey pucks) allow the jack to be precisely aligned (and stay aligned when adjusting/jacking) with these positions and provide a standoff between body and jack to prevent the jack from damaging that small key section of bodywork. Some jacks will be worse than others, but you sometimes don't get a choice with what is being used to lift your car. Keeping a set on board and informing the person doing the jacking that you wish them to be used will mean that the jack point and surrounding bodywork should be protected no matter what is being used for the lift.
Lots of threads with lots of different solutions, but this one has pictures to illustrate the potential issue
Jack Points - notice how the small safe area is in the diagram. IMHO, without seeing area, my feeling is that the proposed device may be a little too big. My current preference is a more solid hockey puck design which should keep things clear of the sill area.