It would be more correct to say Ilberd and his countrymen summoned Shinryu. It was all of their dreams to see the Empire crushed, and their deaths/dreams served to summon Shinryu, with Nidhogg's eyes as the conduit of aether needed.
In general Final Fantasy lore Omega and Shinryuu are both extra-dimensional beasts locked in an eternal struggle. It was really good for Yoshi-P to have brought that story here in all it's glory (also leaves him a large berth of space to write a backstory for Omega as we do it's accompanying raids. I mean we could literally do raids anywhere in the Final Fantasy's lore (across any FF game really) if the Omega story holds true.
Also Yoshi-P said it will be 2 years between Stormblood & 5.0 so take it as you will.