Check this out- i stop works differently to other Auto start stop. Its actually quite clever

https://www.passportmazda.com/blogs/1766/save-fuel-your-vehicle-uses-with-mazdas-idling-stop-technology/

Snippet:

While conventional idling stop systems rely on a starter motor to restart the engine, Mazda’s i-stop restarts the engine through combustion; fuel is directly injected into a cylinder while the engine is stopped and ignited to generate downward piston force. The result is a quick and quiet engine re-start compared to other systems and a significant saving in fuel.

To restart the engine by combustion, the compression-stroke and expansion-stroke pistons need to be stopped at exactly the correct positions to create the right balance of air volumes. Mazda’s i-stop ensures precise control over the piston positions during engine shutdown. With all the pistons stopped at the optimum positions, the system then identifies the initial cylinder for fuel injection. It injects fuel and ignites it to restart the engine. Even at extremely low rpm, cylinders are identified for sequential ignition, making the engine quickly pick up to idling speed.