Could you clarify the question? I'd answer more thoroughly, but my main argument (not a very structured one, but I think a justified one) would be that Kefka Palazzo was of unsound mind; justification for his actions comes from personal motive, greed and desire to obtain the esper Valigarmanda.

He was initially acting under the command of Emperor Gestahl, but at the time of the final invasion of Narsche, his motivation seems to have been power (FFVI, GBA version). His first association with the locale--sending Terra to the kingdom of Figaro--was ostensibly motivated by the frozen esper, a mission which failed with the awakening of Valigarmanda (spelling?).

As to why the kingdom of Figaro stood by and allowed an invasion of their lands, though, my most educated guess is that Kefka and the forces behind him, both military and imperial, are forces to be reckoned with, and there have been repeated examples of the general populace standing back and letting dictators do their thing unmolested (e.g. Shin-Ra Electric Power Coop., sEED, and Org. XIII). It's a trope in history, and that's quite seriously my best guess as to why the kindgom of Figaro stood by and allowed the invasion.