I'm definitely not an expert, having only had success with Medusa thus far. In my experience they will leave during/shortly after preparing for an attack on the city.
According to reports (ex.
http://wiki.ffxiclopedia.org/wiki/Talk:Gulool_Ja_Ja), the NMs will repop 1 hour after besieged has concluded.
It is also possible that the NM may not respawn as quickly as reported if they are defeated during their attack on the city. I believe this extends the repop timer considerably, but have done no testing to confirm this yet. Anyone with facts on this, please comment! I only know that I have waited well over an hour for these NMs to return.
BTW this guide is pretty handy for those that haven't seen it (not mine):
http://staticls.guildwork.com/wiki/p/toau-kings
EDIT: Just found this forum post which I think may be relevant:
http://www.ffxiah.com/forum/topic/27814/medusa/