Yeah, it's something they actually extended from XI -- The goldfish mobs as they're known were one of the few in XI that were "aggressive" to you but never attacked, so clearly they have hate on you; Same with the Lycopodiums (pink flower mandragoras) but all they did was follow you and if you did a certain quest they'll cast a type of regen on you.

In XIV some mobs like Drakes will literally 'warn' you if you're too close before striking and if you don't take said warning you'll be dead in a few seconds.