
Dark Nero |
1) There was a FAQ related to interaction of the Ivory Labyrinth location with the Groaning Gate barrier:
https://paizo.com/paizo/faq/v5748nruor1h4#v5748eaidgsgn
After you resolve your encounter with a bane, immediately move to Blackburgh.
If defeated, you may examine the top card of your location; if it is your turn, you may explore your location.
This FAQ means that we finish the encounter by fully resolving the "resolve the encounter" step of the encounter, at this point the encounter is over and we not have 2 pending effects to resolve:
1. "after you resolve the encounter, immediately move..."2. "if defeated, you may examine the top card of your location..."
In this case, the reason why movement is resolved first is clear - because it has the word "immediately" in its text. But what happens if the "if defeated" power of the defeated bane also has the word "immediately"? For example, you defeat the henchman "Cultist of Baphomet" at the Ivory Labyrinth? This henchman says
If defeated, you may immediately attempt to close the location this henchman came from.
In this case we have two effects that are triggered at the exact same moment:
1. "after you resolve the encounter, immediately move..."2. "if defeated, you may immediately attempt to close the location this henchman came from."
I cannot determine the order of these triggers based on the MM rulebook and the latest FAQ.

Brother Tyler |

In the Ivory Labyrinth/Cultist of Baphomet instance, the sequence doesn't really matter.
My interpretation...
Moving to Blackburgh happens regardless of the type of bane you encounter.
In the case of defeating the villain or a henchman, after moving to Blackburgh and permanently closing the Ivory Labyrinth* you would then move to a random location.
* There's a FAQ or discussion somewhere that makes it clear that you can attempt to permanently close a location even if a power moves you to another location before you get to that step. At least, I think there is. I'm going through the FAQ now to find it. In the case of the Ivory Labyrinth, "attempt" isn't the right word since all you have to do is discard 3 cards.

skizzerz |

If multiple things happen "immediately" then you choose the order you resolve them in.
That said, if the game doesn’t specify an order for things, you decide the order.
Note that any effects that grant an additional exploration must be taken "immediately" and implicitly have that timing.
If a card grants you an additional exploration, after you finish what you are doing, you must immediately use that exploration or forfeit it.
For Brother Tyler's aside, the rule is the opposite: you can never (attempt to) close a location that you are not in.
You can never attempt to close a location that is temporarily or permanently closed, or that your character isn’t at.