Most departments have a tone notification over the alarm system at shift change. The departments that I a familiar with have an "alarm systems test" at or near shift change. The tones going off is recognized as official shift change, so it is the responsibility of the previous shift if the tones have not sounded, and the next shift if they have. If that occurs right at shift change, the official determination is made by the dispacher, whether or not he/she has done the tones for the morning.
Additionally, because shift change, at least in my area, is very early in the morning, the call volume at that time is generally the lowest of the entire day.
The actual practice is different though. For example, there was a structure fire, which are rare, at shift change, so firefighters from both shifts went.
I hope this helps with your story. Let me know if I can be of additional assistance