Sign and the first 4 games most certainly did not happen at the same time. No where near at the same time. The end of the anime has Aura finally awakening as well as Skeith awakening as the First Phase. The games start off with Aura being chased by Skeith. The games don't even start until sometime after(a few months???) the series ended.

.hack//Liminality took place at the same time as the games but in the real world and it was a short OVA bonus thing. One disc came with each game.