With Gix, the ability lets you cast the spells as part of its resolution, as the ruling you shared notes. It's basically saying "Exile the cards, and put any number of them onto the stack." You don't get the ability to do this at a later time, only right as the ability is resolving. Since that would preclude casting anything but instants, it has to bypass timing rules by necessity to function as intended.
Xanathar doesn't do this - it gives you an ability that you didn't previously have (playing cards from the top of your opponent's deck) until the end of the current turn. The pertinent wording that is absent from Gix and tells you which type of effect you're dealing with is the 'Until end of turn, you may...'