ok. remember this.
After the light goes off, the alarm is set [duh you know this. others may not though

]
If you window is down, you can open your door from the inside and it will go off.
If you unlock the door MANUALLY and open it, it will go off.
until...
you put the key in the door and unlock it like that.
Most key FOB's [see below] have an alarm or trunk function on them.

the orange is what used to be my alarm button. i ripped it out. got tired of hitting it. good news is my trunk button does the exact same thing. it turns the alarm on and off. it gets annoying at times.
I discovered mine had a car alarm by accident. Took me a minute to turn the alarm off until i realized "put the key in the door and 'unlock' the car".
If you get another FOB, you can program it to your car [there's another section that tells the right sequence], just make sure it has the alarm feature you want and you're good to go.