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...'

FYI I don't think the bot is looking at post titles but this is a good update I will add in later

@Worx There are two ways these abilities are worded:
* Permission to play/cast a <set of cards> in a given <time period>
* Instruction to (optionally) play/cast a <set of cards>.

Technically neither grants you the ability to casts spells as an instant. The first doesn't alter the timing of playing spells at all, just gives you the ability to play them from an unusual place (the usual place is from your hand). The second instructs you to cast the spells while the ability resolves, usually you can only play spells (or abilities) when you have priority (and no player has priority while a spell/ability is resolving).

The two wordings are similar, except that the permission version lists a period of time (until the end of your next turn, while the cards are in exile, while ~ is in play, etc). Use the existence of a period of time to figure out which type of ability it is.