#jojojump13

In this bit (and the source which that line comes from) is more referring that in Ancient Greece, Eagles were basically another version of the Phoenix, that were a symbol and had the power of rejuvenation; as Phoenixes also popped up in Phoenician, Egyptian and Persian Mythology so somewhere along the way, all of those areas had the idea of the phoenix pop up or it got absorbed along the way.

Anyways, Hebe being the child of Zeus, the eagle represents as well. It would probably be more common for the children of Hebe to communicate with eagles or have an affinity with them; since well, Eagles are a lot more easier to come across. There's also the fact that the children/legacy of Hebe/Juventas (roman god equivalent of Hebe) are going to be more in turn with the giant eagles at Camp Jupiter's Aviary. Maybe being able to communicate with them well enough to ride them like that they did in the Lord of the Rings and the Hobbit; where they all rode the giant Eagles across with the dwarves, hobbits, and a wizard.

If they do come across a Phoenix, I can't deny that they could communicate with it and they sort of belong in the same realm. However, like most mythical creatures, I wouldn't be surprised if the Phoenix has a more intelligent and individualistic personality as it has lived and died over and over, and just as old; so if the children of Hebe want to control, borrow the power of the Phoenix, well....they best be ready.

Power wise, I can see a rare power a child of Hebe could have that may seem Phoenix like; is being able to have the power of regeneration? sort of like Wolverine or Deadpool. However, unlike those two who are like Level 100 power scale, the child of Hebe would have like a Lvl. 30? They can regenerate wounds to a certain degree, but they wouldn't be able to regenerate lethal wounds (i.e. stabbed in the heart), especially if they're really wounded and exhausted. Maybe they can regenerate an organ but it'll take a lot of power and shave down their lifespan but hey who knows. Best not take any chances or bet being able to rise out of the ashes, at least not alone that is.