but somehow my 2018 Clarity gasoline engine turns on without the hybrid mode by itself even when the big battery is fully charged, I thought it is for charging the 12v battery.
Any feedback will be appreciated.
The gasoline engine can turn on for various reasons even with a full traction battery. But charging the 12V battery is not one of them. The 12V battery is charged by the traction battery via the DC-DC converter. This occurs anytime the car is in READY mode, even when the engine is not running.
The gasoline engine will turn on with a full HV battery if you press the accelerator past a certain point. Even if you only do this for a brief moment, once the engine starts it will remain on for a few minutes until it warms up, then it will shut off again.
Another situation is when you leave home with a full battery and within the first mile or so do any kind of regen like using the paddles or pressing the brakes, since the HV battery is full it has no place to store the electricity being generated by regen so it spins the gas engine to dissipate the energy, this causes the gas engine to start up and once started it will run for a few minutes until it is warmed up.
Some people drive relatively short distances each day and almost never use the gas engine. After a month or so of not being used the gas engine will start up on its own and go through a warmup cycle.