For some reason, your mind has the ability to accept tiny bits of input from the outside world, and still remain in a dream state, while incorporating these elements into the reality of the dream. This is the same reason that some people can hold a rudimentary conversation while they are sleep talking. This is also the same reason that when someone has their hand dipped into cold water, they dream about water or about using the bathroom. The alarm can be incorporated into your dreams in the weirdest ways sometimes. You could be riding a dinosaur who then opens his mouth and emits a strange beeping noise, or an alarm could materialize out of nowhere in the context of your dream and start going off.
Cues such as this usually occur for a brief moment while a person is asleep, but will eventually reach them and bring their mind back to reality enough to let them realize that they need to wake up because their real alarm is going off. People with more active imaginations are unfortunately at fault here. If the alarm sound enters their dream, but they are able to come up with a creative use for the noise in the context of the dream, then they might continue on dreaming while the alarm turns itself off in the background after beeping too long. It is fairly common for people to sleep through their alarms, or at least more common than it should be for a career professional.
An actual alarm going off is not always the reason that one might have a dream about alarms though, since an alarm represents coming to your senses, and waking up, the alarm might show itself as a symbol to bring you back to your senses. You need to accept what is going on around you and know that you are in a bad situation. Your dream is warning you not to be so naïve, you need to “wake up” and realize what is going on around you is not all it seems to be. Do not be so naive. A bit of experience and common sense will sever you well in life.
If in a dream you are pulling an alarm to get the attention of others, this could show that you are feeling anxiety over something that is going on in your relationship. You feel that you need help but do not know who to turn to, so you pull the alarm for the attention of anyone who will listen. Alternatively, you could be pulling the alarm because you feel like no one is listening to you in waking life and you want to make your opinions and beliefs known.