The alarm is expecting that the wire connected to the interior light is held a 12 V when the doors are closed. The circuit they show has an incandescent bulb holding the wire at 12 V.
If:-
1) Your car has LED interior lights, or
2) the door switches only go to a control box, or
3) the power to the interior light is removed after some time
then the alarm may false trigger.
I suggest that you try a resistor, 1k Ohm would be fine, between the battery feed and the door trigger. The resistor will keep the voltage up near 12 V and there should not be any more false alarms.
That alarm is designed to fit cars that have got all the door switches wired together, and directly connected to the interior light. I don't think I've owned a car like that in the last 20 years, maybe 30, as all modern cars have LED interior lights, fading on and off of the lights, a delay after closing the door before the lights go out, a timer to shut off the interior lights if a door is left open or any combination of those. The electronics in modern cars do all sorts of things with the interior light that would stop that alarm working in the intended way.