I haven't done the Omega raids so I can't form an opinion on what may or may not have been mentioned in that storyline, but magitek does utilize aether in a more roundabout way, in that cereleum contains aether itself (it's basically liquid aether processed into a refined form, making it very analogous to mako energy in FFVII, more so given the aetherial sea in FFXIV is also called the 'Lifestream'.).

It's to compensate for native born Garleans being unable to manipulate aether from their bodies themselves (as in, magic, hence the 'magi' in magitek), so they use processed aether instead to power technology like airships.

Aether is the energy of reality itself, and there are many different means to manipulate or utilize it with different results, from Disciples of Magic to even MCHs' using their aethertransformers to form aetheric bullets from their own body's aether. Teleportation is also the manipulation of aether, in that when a person teleports they break their body's physical form into aether and travel through the Lifestream instantly to an aetheryte which acts as a beacon in the aetheric sea.

Really, all that is needed to manipulate aether is a will and enough aether to do so, the ultimate expression of that being Primals.