This seems to be a common problem for a lot of people, including myself, if the bug reports/comments sections on nexus are of any indication.
Probably a patch or something broke it. Who knows?
Either way, I do have a temporary "fix" here:
https://www.dropbox.com/s/f8etn6t562wvxtf/SimSettlements_AddOnPack_Defences_Brae.esp?dl=0
Be warned: I use "fix" very loosely. While it does solve the problem of artillery not functioning, it instead gives you the exact opposite problem: Now artillery guns in plots will function regardless of whether or not someone is occupying them, which means you'll have to employ self-restraint to prevent yourself from cheesing this system. Still, it's marginally better than it not working at all.
Hopefully though this should be enough until Brae comes back and finds a way to fix this properly.
(Btw, I've ruled out any sort of mod conflict. I uninstalled ALL my mods (thanks Mod Org, otherwise this would be hella awkward) except Simsettlements, Industrial, and this mod. I tested flares straight off, no-go. Refreshed plot, no go. Rebuilt plot, no go. So it's not a mod conflict of any kind.)