Unless they are volunteer firefighters, they won't show up at the firehall.
They are just responding to the howl of the siren. some guys go out in the night and use a siren to locate coyotes then come back the next morning to call them.
I think most people overthink this coyote killing. There's a ton of things to be aware of, but if they were as smart as some think they are they would never get shot.
I can howl at my place after dark or at dusk and get a vocal response from a dozen or more coyotes from 4 different directions and not have one come in.
Depending on which month I can get those same coyotes to come in on the run to beat me up and take my lunch money with the same howler.
Get someone who can call to go with you. they call you shoot them with the pointy stick. rinse and repeat.