In-multiverse explanation: There are several different "universes" within the Marvel Multiverse, and each of these vary slightly. In some, the X-Men were wiped out by sentinels, etc.
The movies are clearly from a different universe than the main comic book universe. You'd expect differences like this.
The fact that this is an alternate universe is even covered by the Wikipedia article on the Chitauri:
The Chitauri are a fictional race of extraterrestrial shapeshifters that appear in publications by Marvel Comics's alternative universe, Ultimate Marvel, in the limited series The Ultimates. They were created by Mark Millar and Bryan Hitch. They were created for the Ultimate universe franchise in place of the existing Marvel Comics alien species, the Skrulls, which play a similar role in the franchise's mainstream continuity. Later, Marvel would choose to distinguish between the Skrulls and Chitauri of the Ultimate universe. The species would later be adapted to other media, notably appearing in the 2012 film The Avengers as an invasion force led by Loki.
All of that merely shows that there are several different universes in the Marvel Multiverse. In the movie, we were simply in a different reality (namely earth-199999). There's no real reason to even expect that the cube is a Cosmic Cube.
The properties are different, and even the Marvel Comics Database indicates that this is different from a Cosmic Cube from the main continuity on the Cosmic Cube page.
Marvel Cinematic Universe (Earth-199999)
Cosmic Cube (Earth-199999)
ADourAdded by ADour
The Cosmic Cube or Tesseract, as it is mostly called, of this reality is a powerful Asgardian artifact created by Odin which possesses the abilities to create infinite energy, which can be used to create wormholes to other parts of the universe and different dimensions, rather than reality manipulation. Unknowngly why, the Tesseract was hidden on Earth.