As an experiment, assuming NRaas mod usage, you might want to try making this sim non-selectable using NRaas MasterController. If you have StoryProgression engaged, that should progress the career of the non-selectable sim in the active household while you are unable to control him.
In this case, and in a couple of other Ambitions careers, I very much doubt you will see him fighting fires and rescuing sims on his own unless some real fires generated by forces other than the career happen to take place around town, as the scenarios generated by the career are indeed designed for active play. But they should still be making a stipend the same as other career firefighters and slowly move up (or down) the career ladder. If you don't like the effect, or if you do want to control him yourself during off duty hours, then this can easily be undone again.
