To be frank, the NPC watchmen autohostile to NPC monsters is buggy.
Its intended purpose, I imagine, was to keep monsters out of areas that are patrolled by the Watch. However, it is now a hassle. Whenever a watchman sees you, they will instantly attack you. You cannot attack them, or do anything to them, without a DM. This leaves the only option anywhere to run, even if you are in a group. While this is not a problem for a lone monster, it is a problem with other bugs take effect.
If a watchmen sees you, they will always follow you unless placables get in the way. The way the script seems to handle it means they will follow you through transitions, through stealth, through invisibility. Which means that you rarely can escape them without attacking or disabling them, which isn't possible without a DM.
The Watchmen are also in weird factions. When I had to attack one that followed me from the Canal Ward, the Bugbear Enforcer turned hostile to me and moved to attack. This can likely easily be fixed by moving the factions around a bit if a DM ever has time, but it is a very small priority.
These three things seem to be bugs with the current system, even if they are caused by others bugs (like the guards chasing through invisibility is not only this, but another bug takes effect). I would suggest changes to this system, so that it is more fair to everyone involved. Since this system was made to prevent the need for DMs to deal with monster shenanigans all the time, I would propose that instead the watchmen return to their posts every three to five seconds after turning hostile. If they are being attacked, this script will usually be overriden, and allow the private to continue attacking after a brief pause. However, it would prevent watchmen from chasing monsters through Lower and the caves, where I doubt they would reasonably be going. It would also prevent any negative consequences of them seeing through invisibility or stealth, as they would return to their posts, and then not be able to see you and so not return to attack you.
I forgot the rest of what I'll say, so I'll probably say it in responce to critiques.