If the alarm does not turn off when you trun the key on, you have an issue with either your key, or the ignition switch\theft deterent module
As stated in your owners manul regarding the security setting option:
If your vehicle has the remote keyless entry system, this feature allows you to select the method used to arm the vehicle's security system. When SECURITY appears on the display, press the reset button to scroll through the available settings:
RKE (Remote Keyless Entry) (default): The content theft-deterrent system will arm when the lock button on the remote keyless entry transmitter is pressed or when the power door lock switch is pressed.
PASSIVE: The content theft-deterrent system will arm itself 60 seconds after the ignition has been turned off and all of the doors have been closed.
See Content Theft-Deterrent for more information.
Choose one of the available settings and press the information button to select it and move on to the next feature.
One way to lock the vehicle and not arm the alarm is to manually push down on the locks. Don't use the remote, or the lock switches inside the vehicle