Is a fire alarm part of security?

Indeed it is. A fire can harm your security. If not noticed on time, such as when you are asleep. A fire alarm will alert you in a building or a house, so you can move to safety on time, so it is part of security, even when the term most often refers to a person providing guard to property or life.

In the commercial sense of security, yes, a fire alarm would normally be part of the security company's job, in addition to monitoring intrusion alarms and other conditions of the particular location.

For another thing, the security department may be responsible for maintaining and testing the fire alarm system, not to mention writing policies and procedures for use in training the various occupants in what to do during a fire alarm.