The Old Gods make perfect sense as minions of the Void Lords. The difference between the two makes sense.
Think about it for ten seconds. The Void Lords are forces of pure cosmic entropy. They aren't lovecraftian outer gods with a pantheon of deities that are unknowable and beyond our comprehension. While they are powerful beyond the scope of morals to comprehend, that's not really their bit and never has been. They are hunger personified.
They are insanely powerful. Dimensius (who was the last to manifest in the universe) essentially beat us while at a pale shadow of his full strength, and would have consumed us without Xal'atath's help. The last raid boss to be able to claim that level of superiority over the player without aid is probably the Lich King, who could've beaten us at any point.
Their weakness? They can't exist in the material world without massive influxes of energy, because they are pure forces of cosmic void. Even simple Voidwalkers can't, unless the veil between the void and our reality is very thin.
The Old Gods are almost the direct opposite of that. They are almost comically tied to their blood and flesh and energies, to the point where they pretty much aren't conventionally killable. Even Y'shaarj couldve come back if Garrosh went unchecked and Yogg-Saron is probably not dead in any permanent sense. C'thun was supposedly on the Old-God equivalent of life-support when we beat him, as he supposedly got a worse thrashing from the Titans than the other two. While he's not waking up anytime soon, and Sargeras's sword probably got him good too, I'd bet money he's not totally dead either and his power is responsible for empowering Cho'Gall into the monster he was in Cataclysm. They're very Lovecraftian in this sense, and human-defined death as a concept seems temporary to them unless they are near totally eradicated.
This makes them almost the perfect minions for the Void Lords, who are impermanent beings with a limited ability to effect the material world and probably have limited chances to actually create them, as effecting the material universe is so hard for them. You'd want a minion exactly like an Old God, to ensure your influence is long-lasting after your brief manifestation. You'd want their corrupting effect to make sure that sheer physical force (perhaps even enough to banish their masters) aren't effective at beating them out and they can outwit and subvert anything they can't beat.
The issue is that they probably made the same mistake as the Titans on this issue. They didn't realize their creations might not actually do what they were commanded to do in all instances. They were also very likely not unchanged by Azeroth's energies either.