How do atmosphere processors work?
To put it simply, it doesn’t matter who builds a processor… only who currently owns it. A processor will slowly change the atmosphere of a planet (rate inversely proportional to planet size) to the ideal preferences of the owner of the processor at a cost of 3 fuel per update, which must be loaded into the processor. The last time I checked, processors will continue to eat up 3 fuel per turn if they have fuel to burn even after a given planet is perfectly atmospherically compatible with the owner, so it’s a good idea to scrap processors once you reach this goal.