I'm pretty sure Apkallu hate works in a way similor to fomors. That's to say that if non have been killed none will aggro but the more that get killed the lager the aggro range [and tp moves change too]. now the difference is that while fomor hate is player based [meaning it's based on the player hate], Apkallu hate is zone based meaning they aggro EVERYONE that passes past. Apkallu are part of trail weapons [axe final is one]. so hate will probably always be there now.
Link EDIT http://wiki.ffxiclopedia.org/wiki/Category:Apkallu
cba sorting link out..... so here is what it says.
Apkallu have a communal hate based on how many you have killed (like Tonberries and Fomor). As your Apkallu hate goes up, they start using a larger variety of attacks. Initially they only use Yawn. After as few as 4 kills they will begin to use Beak Lunge, and will begin use of Frigid Shuffle after approximately 15 kills. They start to react violently to White Magic (including attacking healers even after extremely low Cures), and become very difficult to kill (gaining both physical and magical damage resistance to the point of near invulnerability). As Apkallu hate rises, their rate of multiple attacks and Counter use will increase as well. It is currently unclear how to lower Apkallu hate rapidly, though it will decrease over long periods of time. Over a 1 week game time period, the hate will decrease by at least 20 kills, possibly more.
Apkallu hate appears to be area based. Which means, if a group of people caused high Apkallu hate in an area, another group which comes later will receive the hate effect. It is possible to trade certain fish (Ahtapot, Veydal Wrasse) to the Apkallu NPCs, which makes them follow you around. Preliminary tests shown that hate raises rapidly with the following NPC Apkallu looking at the player killing other Apkallu. Also, after a certain amount of hate is accumulated, the NPC 'green' name will turn yellow indicating that the player has accumulated a large amount of hate. NPC Apkallu does not seem to appear when there is high hate in an area.