This is war we're talking about. Full-scale war, not the skirmishes we've had with the Garleans throughout Heavensward and not Operation: Archon against the XIVth. As a whole, however, the Grand Companies (which are the only forces that have the structure needed to properly oppose the entire Garlean military) are more than likely not going to execute survivors, POWs, and noncombatants.
There's no guarantee that won't happen - even modern militaries, with all the tech and oversight we possess, still have soldiers commit war crimes. However most the groups listed - Ilberd's turncoats (which consist of... himself, Laurentius, and Yuyuhase and that's it), the Ala Mhigan resistance (a guerrilla faction), some of the Lominsan pirates, and the beast tribes are a far cry from proper militaries and would be utterly crushed if the Garleans decided to decisively deal with them. (The Elementals, who knows? They're content to let dying people... just die though, so roll the dice and see what comes up.) Aside from the Gration's engines being frozen, there is literally nothing preventing them from using it to blast the Vanu Vanu (and other beast tribes) to smithereens.
If we want to win, that means standing together... and the Grand Companies are the only ones who have the structure to do so, meaning we'll play by their rules. Meaning no executing survivors, POWs, and noncombatants - or at least that not being an official policy and an offense worthy of court martial (that will get you a lifetime in prison). Again though, no matter how hard you try to avoid them, war crimes are inevitable on both sides. There are no real survivors of war - just the guilty and the dead.
In the context of the lingering remnants of the XIVth Legion, though... I don't think there's much to worry about.