I posted this little diagram to another thread not too long ago. While it's a schematic for an ATO, not an overflow prevention kit, it's wired much the same, using the same components. It also works much the same, you simply need to ignore the extra parts of the ATO that is designed to constantly switch the supply pump as opposed to only shutting it off in the event of high water level. I guess it also differs in that there's no LED indicator or reset switch. There's also what's called a 'latching circuit' involved on the ATO version. Nevertheless, it's a good visual of how something like this should function, using low voltage (12VDC) & a relay to switch a pump running on 115 VAC.
If you can imagine this circuit with only one float switch, add a reset switch & LED light, it will be pretty close to what your pump stopper kit does. Oh yeah, instead of it being a top off pump, the pump in your case is the sump pump. An ATO is designed to turn pump both on & off, whereas your pump stopper is designed to turn it off only & then you must reset manually using the pushbutton switch. So in the above diagram, eliminate FS1 or actually try to imagine FS1 as a mechanical reset switch, instead of another float switch. Follow?? Now the only thing missing is the LED light. Actually the LED light could be replaced/complemented with a buzzer, that way you have an audio warning instead of a light which you may or may not notice.
EDIT: I guess I should add my own CAUTION here & advise you not to use this schematic directly to figure out your particular pump stopper, since the float switch in your case may be wired differently. The instructions mention something about flipping around the float & I haven't bothered trying to reverse engineer their hookup instructions to see if the relay is wired normally energized or normally de energized. I would guess de energized, but like I said, I haven't deciphered the instructions to that degree. OK, sorry EDIT 2: First part of instructions say the float switch closing, energizes the 12 volt relay.