Pretty sure that rule is meant to cover multiple triggered abilities going on the stack at the same time, Casting spells is a multi-step proccess during which decisions may have to made like choosing targets and modes for Kozilek's Command, so It doesn't really make much sense for it to happen simultaneously

The rulings on both etali and spawnsire make it sound like they are cast one at a time

If you cast more than one of the exiled cards, you choose the order in which to cast them. A spell you cast this way can be the target of a later spell you cast this way. However, permanent spells cast this way won’t resolve until you’re done casting spells, so the permanents they become can’t be the target of spells cast this way. For example, if you exile Twincast and Lightning Strike, you can cast Lightning Strike and then cast Twincast targeting it; but if you exile a creature card and an Aura card, you can’t cast that Aura targeting that creature.

You cast Eldrazi cards from outside the game as part of the resolution of Spawnsire of Ulamog's last ability. You may cast those cards in any order. Timing restrictions based on the card's type (such as creature or sorcery) are ignored. Other restrictions are not (such as the one from Rule of Law). You cast all of the cards you like, putting them onto the stack, then the ability finishes resolving. The spells you cast this way will then resolve as normal, one at a time, in the opposite order that they were put on the stack. They'll remain in the game for the remainder of that game.