I still don't think it's complex at all. People know how a healer works. The damage guy is super simple. Support is buffing. Trapper is only more "complex" because of his or her crucial role, but let's be honest the basic trapper is easy as hell. You shoot, follow your thing, lay down "mines" that slow the monster and you can create a bubble that keeps the monster from fleeing. Play your role and everything will be fine. Payday is more complex if you want to stealth levels than Evolve is ever.
Payday is about getting your gear, stealing some loot from inside a building, and getting out before the cops show up and kill you all.
you can play that game with anything if you want to. Dwarf Fortress is about building a keep and maintaining it against all sorts of opposition, be it natural or otherwise.
Evolve has some depth to it, you can't describe it or help someone through it without sounding like some sort of stiff nerd because there no way to say "hey, go back and check that fake rhino out. There's a perk you can now access from it that you'll find helpful in this match" without kinda sounding like a stiff dork about it. That's also an example of how different Evolve is from your typical first person shooter in that it has a lot of things going on and going for it that you're not going to find in your average online FPS game. I can hand my cousin a controller and ask him to play COD and regardless of what version of the game it is he'll do ok. I can't do the same with Evolve because he'll end up costing his team the match for quite a while until he wraps his head around it.
So yeah, this isn't Ratz Instagib where you kinda know what youre doing within 5 minutes and that's just about it. Whether you find this to be more or less complicated than your average gaming experience is pretty subjective. But you can't call it "dead simple" and be left wondering if you've dipped into the hyperbole pond or not because you're at least knee deep with that statement.