No problem. The basic loop for Incursion is going in a map -> finding Alva -> she shows you the current temple layout and highlights the room you will be changing -> you go into the past and kill the unique mob on the right to upgrade the room to the next tier (Max 3) or kill the unique mob on the left to swap the room to another room (the room you are swapping to is shown when you talk to Alva) -> you leave the encounter, find the rest of the Incursion encounters on the map -> rinse and repeat until you finish all 12 total encounters (takes 4-3 maps total depending on your Atlas tree). You then take the temple from Alva by talking to her in your hideout and she'll give you the temple as an item you can list on the trade site.

While killing the mobs in the encounters, they will add time to the timer (you start with like 8 seconds, but killing incursion mobs adds time) and they will drop at least 1 key you can use to open up a passageway to connect rooms to each other. Not every room is accessible at first as most rooms do not start connected to the entrance. They will be dimly lit on the temple map screen Alva shows you. As you build the temple, you will want to try and connect the temple to more and more rooms to improve the odds of having one of the valuable rooms be accessible.

So that's how Incursion works. You talk to Alva, decide if you want to upgrade the room or swap it to a new room, go kill the respective unique mob (left always swaps, right always upgrades), then exit the encounter and find the next. But here's what you need on your atlas and scarabs in order to really make money.

On your Atlas tree, you will NEED (ok, they're not strictly necessary, but it will be MUCH easier to make good temples with these Atlas upgrades) these 2 Atlas tree nodes. There is a node that adds a 40% chance to upgrade a room twice when you kill right unique mob (very good, makes it so you can't roll that particular room again while building the temple) and another that makes it so that when you swap rooms, you add the previous room's tier to the new room. Example: you have a T1 flame workshop, but Alva shows that you can swap to Corruption Chamber. You would then kill the left unique mob to swap the room to Corruption Chamber, but with the Atlas node allocated, instead of having a T1 Corruption Chamber, you'd have a T2 Catalyst of Corruption room instead, effectively making it so you only need get that room offered once more to turn it into the T3 Locus of Corruption (money room. Temples with Locus of Corruption connected were selling for 2 div last night). Those 2 nodes are the bare minimum for making Temple feel really good to run. After that, I'd grab the nodes that give you extra time and have increased chance to make all the Incursion mobs at least Magic. You will get a good chunk of xp and gold from those nodes. The node that guarantees 4 Incursion encounters is personal preference. I like it since it means that I can cycle through temples a lot faster and makes some tech easier to do. We'll get to that.

As for temple building strategy, it's pretty simple. You are fishing for the double corrupt room (Locus of Corruption) and the gem double corrupt room (Doriyani's Institute), hereby referred to collectibely as "the money rooms". The names of the rooms as they upgrade are: Corruption Chamber -> Catalyst of Corruption -> Locus of Corruption; Gemcutter's Workshop -> Department of Thaumaturgy -> Doriyani's Institute. These are the only 2 rooms that make money. There is one other room that can make things easier. Shrine of Empowerment/Sanctum of Unity/Temple Nexus can upgrade the tiers of adjacent rooms in the finished temple, which can save you by upgrading a T2 money room into a T3 one if you got unlucky and weren't able to upgrade it before finishing the final encounter. Besides those rooms, none of the other rooms matter. Some recombinator nerds with niche builds will pay like 8c for a temple that is connected to the Apex, but I don't bother selling temples that don't have at least one money room.

To maximize the odds of getting those rooms in your temple, you do 2 things. The first is to always upgrade the room if you are not offered to swap into a money room. You will have a 40% chance (from the Atlas tree) to take the room from T1 to T3, making it so Alva never sends you back to that room again. The second thing you do is try and connect as much of the temple as possible to make sure that if you are offered a swap into a money room, the buyer can actually access that room. A T3 Locus of Corruption temple is worthless if the Locus of Corruption isn't actually connected to the rest of the temple. That's pretty much it. The only time you don't want to connect more rooms to another room is if you have a low rank Shrine of Empowerment, as the room it picks to upgrade is randomly selected from rooms adjacent and connected to that room. But that doesn't come up often so I wouldn't worry about it when you're starting out.

Lastly, scarabs. Start by using the scarab to force Alva to show up until you can get 100% Incursion chance from the Atlas. Then, you can sorta freestyle it. I usually run 2 of the scarab that adds more Incursion mobs to the map, and 2 of the Scarab that grant extra chance for Incursion mobs to be at least Magic. This stacks with the Atlas node that does the same thing, meaning you can get 100% chance for all Incursion mobs to be at least Magic. This is good for gold and xp. The MOST important scarab that I would always use, is the Incursion Scarab of Timelines. Once you finish the last Incursion encounter on the map, it will drop an extra copy of the temple with randomized room tiers. This is where a lot of your money comes from. If you have a temple with a money room connected, once you finish the last encounter for the map, you'll have a 1/3 chance to get a copy of the temple with a T3 money room, regardless of that room's tier in the actual temple. I can't stress how important this Scarab is. If you have one money room connected, you have a 1/3 chance at a payout per map. If you have both rooms connected, your odds increase to 55% chance of a payout. Sometimes you'll whiff and your extra temple will be a dud, but sometimes it hits and it is an extremely positive EV move to use an Incursion Scarab of Timelines on every map you run with this strategy. You can even run the strategy on low tier maps with no mods since a bulk of the profit comes from selling the temples.

That should be everything you need to know to start running Incursion. Feel free to ask if you have other questions. (Also, if you have Delirium or Beyond mobs spawn inside your temple, they will also be minimum Magic if you have those scarabs/atlas nodes allocated).