On my new Jeep, if I lock it with key fob and unlock with the key, damn alarm goes off. So just use the fob all the time.
My neighbor has the same issue, and since English is not thier first language, I was called to assist. It is designed that way. Using the fob to lock the car sets the alarm. Using the key wirhout cutting the alarm will set it off. This prevents stealing your car by slimjim or lock picks.
As to "how secure is my fob?" There are more cars than there are codes, so duplications do occur. It is possible, to drive around a parking lot full of cars, and one might respond to your fob. There is a worse issue with the proximity keys, than the fobs. There is a very cheap range extender that thieves can carry, and your keys inside the house will unlock the doors and start the engine.
