In defense of this, while the Beast Tribes WERE summoning in direct response to Garlean invasion, in theory if the Garleans were SUCCESSFUL in their invasion, they would slaughter every Beastman, and there would be no one left to summon. It's all due to those pesky Eorzeans getting in their way and stopping them from performing the much-needed genocides that the Primal problem wasn't resolved in short order. (Or, at least, that's the official company line.) So, assuming Solus was a human and not out to cause chaos for chaos's sake, it's not totally beyond the pale to assume that he was willing to weather a couple summonings in the short term to put and end to summoning FOREVER.
As for the Burn, even if the Garleans hadn't any personal experience with Primals, they have scholars, and the peoples they conquered also had scholars. There's any number of ways they could have learned about the Primals' aether-sucking nature. They advance to the Burn, are alarmed, and ask the Scholars of the are what's up with that. "Dunno," say the Scholars, "But we theorize it could have been due to Primal summonings? Apparently there were quite a few back in the day..." And the Garleans latch onto that like starving dogs on a steak, because not only does it give them a noble mission, but one that lets them expand their empire EVEN MORE, beyond just the nations that oppressed them thousands of years ago...
We know now none of that is the true motivation, but even had there been no Ascian involvement, it certainly COULD have been. Personally, I think the whole idea of Solus being an Ascian, and the Garlean Empire an Ascian tool, is a RECENT decision made by the storywriting team, not one that's been in place since the beginning. If that's true, then back in the day these motivations would have been genuine...
Why is it unreasonable to think that Ascians are capable of hiding from one another? To date, we haven't witnessed any evidence of Ascians possessing some kind of "Ascian sense" to identify each other. It could well be that while wearing a human's skin, an Ascian looks just like a human, even to other Ascians. I think it's quite possible - even likely - that Varis is Ascian-possessed, and hiding that fact from Elidibus. As long as Varis keeps spouting Varis-like lines, like "Man's destiny is his own," Elidibus will be none the wiser...