We don't have any explicit information that the Ascians have helped any advanced civilization on a grand scale like the Allag. However, it's entirely possible whispering in the ears of Allag about Dalamud and the Heart of Sabik isn't much different than Lahabrea whispering in Gaius' ear about the Ultima Weapon. The First, Second, Fourth and Fifth Astral Era histories are large unknowns, but in the Third, Sixth, and Seventh we do have an "advanced civilization" in each one. Allag, Mhach, and Garlemald.
Should the Ascians be in direct opposition to Allag imprisoning Primals--there's a contradiction. An unknown gang of Ascians specifically gave Allag "the means to entrap" Bahamut. There wasn't much room for interpretation in Tiamat's words.
I'm a subscriber to Ascians definitely helped Solus with the conquering of Islabard just because of what it caused: a shitton of war. Grand wars seem to work favorably for the Ascians and their necessary "chaotic confluence." You elevate one people far above the others so that they seek out and subjugate the myriad masses then pull the rug out from under their Empire. They help you set up the Jenga tower just so they can knock it down. It's probably a case of it's easier to knock down one huge tower than a bunch of little ones-- I don't know I'm not a crazy semi-immortal in a black robe. All I know is the Ascians like conflict. Preferably with an increasingly dangerous arms race. They don't want one side to win, they just wanna ruin everyone's day.
As for the Mhach, that's even more conjecture on my part. The Ascians seem keen on helping people summon voidsent or summoning voidsent themselves. Why? Your guess is as good as mine. Probably something to deal with disrupting the aether of Hydaelyn, since so many voidsent love to feed on it and is easier to pull off than a Primal summoning. The three nations during the War of the Magi seemed to be pretty equally "advanced," but only the Mhach had something like the Void Ark. There must be some degree of aetherscience behind getting that to fly. The Nymians had their clockwork/stratagems and Amdapori their soulkin/conjury but it really feels like the Mhach were, well, the enemy.
Let us not forget white magic was invented in response to the use of black magic--the Mhachi had already began using the land's aether against their enemies. The magical arms race began with the Mhach! It is somewhat curious that in the Third and Seventh Era the advanced civilizations were 'technologically' advanced while the Sixth was 'magically.' Maybe it's an odd/even thing the Ascians do to keep things fresh. Fostering wars seems to be a big Ascian thing.
This does, of course, rather unceremoniously allow some "well then Solus, Xande, Thordans I & VII aren't all bad! it was those dastardly Ascians!" I... meant... to just post that bit about Tiamat and the Ascians knew exactly what the Allags were going to do with Dalamud... and that Bahamut wouldn't be considered an "elder primal" during the Third Astral Era (when he was captured by Omega)...