The Spectral Heroes in the Heroes' Gauntlet (I wouldn't call them 'Warriors of Light' just to avoid confusion, there's a few figures with that name running around at that point) come from nebulous elsewheres, but nothing suggests that those 'elsewheres' would be anywhere further afield than the shards. Thanks to Hildibrand we can confirm one of those elsewheres was the Source, but at the same time I would also put forward the Spectral Dragoons; Dragoons also only exist on the Source. And if Elidibus' ability lets him pull across shards, there's no reason he'd limit himself to one shard.
Beyond that, though, I think it's a mistake to assume that the Spectral Heroes are anything more than just a copied image of a hero. Hildibrand wasn't, sure, but we already know that Hildibrand is rarely a strict adherent to anything we'd call 'rules'. In fact, even with this example he seems unusual; he persisted on the First after all of the events surrounding Elidibus finished and all the other Spectral Heroes dissappeared, suggesting that the rest of them were rather more ephemeral than him. They also seemed to have a lot less autonomy and willfulness, so it seems to me they were just images, and Hildibrand was, as always, a weird exception.
With the fact the Spectral Summoners only summon a red Bahamut, I think it's also folly to assume that they're actually using the same school of magic that we are. Remember that when appearing in the Gauntlet they use the term 'Ink Mage', which is... well, not a Summoner. (Someone told me that Ink Mages appear in some Heavensturn quests, but that's a difficult thing to confirm.) It's likely this is just an entirely different combat style that happens to look similar, like how Aymeric isn't a Paladin but nonetheless uses similar skills. Despite actual dragons only being on the Source, there's draconic things elsewhere; there were dragon-like enemies across the First, there's the gwibers, and somehow there's the Five-Headed Dragon in the World of Darkness. Who's to say that the Fifth didn't coincidentally invent Red Bahamut?
I don't know why time travel is being admitted into evidence here, I think it's a red herring. Time travel is an infamous blind spot for the Ascians; most of them didn't know it existed, and Elidibus only learned the Crystal Tower could do that in Endwalker, while stuck in it. With the Spectral Heroes making their appearance before Elidibus even got to the point of controlling the tower, time travel isn't even remotely possible.
EDIT: And while completely unrelated to the core subject of the thread, FFXIV's time travel is actually really simple. You just have to remember two things:
A: It's possible to either make a stable time loop or a new timeline; if you do the latter, the original timeline is orphaned and can't be returned to (at least, with the technology we have).
And B: that the only figure who understood the actual rules of time travel sealed themselves in a time bubble. Everyone else is just crossing their fingers and hoping for the best.