I wouldn't want anyone to wire a smoke detector to an AFCI breaker in my house let alone anyones. If the breaker works and turns off the circuit, it would have done it because it sensed an overcurrent condition or an arc fault. Hopefully this arc fault that it sensed doesn't start a fire because if you don't have a battery backup in your smoke you might just have a very long sleep.
Battery backup smoke detectors are and should be a requirement. They are required here, as well as to be interconnected, with any new construction and in a remodel if feasable. If they can't be interconnected, then a hard wired/battery backup detector must be installed in all bedrooms, halls and common areas. If an arc fault occurs on their branch circuit causing a fire, the battery will allow the detector to do its job. If the battery is dead, the detector will have signalled with a "beeping", alerting you to change the battery.