Abyssal Artifact Recovery involves multiple rounds of clearing the same asteroid field, with each round getting faster and more NPC Drifters, Rogue Drones, and Triglavians spawning.
Each time you clear the full grid in time, you get rewarded a payout. There are nine rounds in total. Every three rounds, the difficulty increases, meaning the time you have to mine the asteroids get shorter by 30 seconds and the spawning rats get stronger.
During each round, when all asteroids are mined, the Warp Disruption bubble will go down, meaning you can warp off. Between each round, there is a 30 break. When the next wave starts, new asteroids spawn in the same locations as before.
When depleting an asteroid, there is a chance that a Triglavian Cache spawns. This needs to be destroyed and the wreck looted before the next next round starts, as the wreck will despawn after two rounds of being generated.
The loot in the caches is quite valuable and can make up a good portion of the total site income. The mined ore is essentially worthless and difficult to carry around and sell when not using ships with a huge cargohold.
If all rounds are completed successfully, the Warp Disruption bubble will remain down. The site is marked as complete. If one waits for more than 60 seconds on grid, a Drifter will spawn from the rift in the center of the site. This Drifter Battleship will destroy you faster than you can blink, so warp off before that can happen.
If you do not fully clear the grid before the round is over, the site will no longer give any payouts. The Warp Disruption Bubble will remain up until all asteroids are fully mined. NPCs will stay on grid.