Once you have reached Act 7, you may encounter Alva Valai. Alva is trying to find the location of the lost treasure temple of Atzoatl using ancient Waystones that begin appearing from the Causeway onwards. With her help, you will travel back in time two thousand years, to the Temple of Atzoatl during its construction. During this time, you can help influence the temple's construction, so that when you eventually find it, it is filled with glorious treasure. You'll only have a limited amount of time during this visit to influence the layout of Atzoatl in the present day, but this time can be extended by slaying its inhabitants. Enemies will not drop loot during your Incursions, but once the timer runs out, you'll be returned to the present-day and showered with loot based on how well you did. There are two primary objectives to pursue during your incursion: Architects and Altars of Passage.
Altars of Passage
Each chamber in Atzoatl has several walls which could potentially allow it to connect to another chamber. Some of these may already be connected, but many won't. If, during your Incursion, an enemy drops a Stone of Passage, you can pick it up and place it in an Altar of Passage, and it will connect the chamber you are in to an adjacent one. This is important, because when you visit the Temple of Atzoatl during the present day, you may only be able to reach the chambers you managed to connect in the past!
Within each Incursion you can find two Vaal Architects. By slaying one, you will allow the other to escape and later develop that chamber in their own vision. If the surviving Architect had previously influenced the development of that room, that room will then be upgraded. If not, then that room will change to something within their realm of expertise. For example, if you land in the Banquet Hall during an incursion and slay the Architect of Fortifications, allowing the Architect of Toxins to survive, the Banquet Hall will become the Poison Garden. If in a later Incursion you land in the Poison Garden and kill the Architect of Iron, again allowing the Architect of Toxins survive, it will be upgraded to the Cultivar Chamber.
The types and tiers of the rooms you help engineer through your Incursions ultimately form the Temple of Atzoatl in the present day. Each room has a different effect. Some are purely positive, while others may put you at significant risk for valuable rewards. By upgrading the Cultivar Chamber to the Toxic Grove, for example, you will fill the Temple of Atzoatl with dangerously poisonous plants, but you will also give yourself the opportunity to loot a unique item that can be found nowhere else.
Finding the Temple
Once you've performed enough Incursions, Alva will discover the location of Atzoatl, and will offer you the opportunity to go there. At long last, you can explore the temple you helped create, and loot it for all it's worth! After you've visited the temple in the present-day, the next time you find Alva in the world, she will offer you the opportunity to start your Incursions all over again, with a new temple layout and with new opportunities to maximise your rewards.