Firstly fascistcrusader, with the ambiguity of language, and the potential inaccuracies there can be between translations, you can't just simply interpret the passage in such a way when the conclusion that you draw from it isn't in any way supported by the original source material. If the creators truly intended the change in setting upon a Summon's arrival to have been illusory in nature, it would most likely have been made obvious, and not subtly included into the text in a way which was clearly never intended to have been analysed as in depth as you have been doing.
You also keep on telling people to play Crisis Core; I have, and nothing indicates that the setting change is in any semblance a product of an illusion - as it stands, the only thing that supports your conclusion is your asinine interpretation of the creators' words.
Now as for why a distinction is made between Gaia and the Summons' dimension in terms of how "real" they are, as should have been fairly obvious, Gaia is the setting in the story where everything takes place, the place that all the characters perceive as being their planet, and exactly what the story's based around, whereas these summons' dimensions are purely temporary locations that -- from the perspective of Gaia and all that is encompasses -- ceases to exist as soon as the summon is no longer in action. They're not part of "the real world" in that sense, not in the sense that they're not physical in nature and act -- and with no real purpose -- as an illusion. As has already been said to you, the very passage that you're basing your conclusion off of, through its use of language, disproves your already silly and unsupported theory.