In FNAF World, we all thought "desk man" was Henry, and the animatronic was Circus Baby before he was killed.
I'm guessing that "desk man" was actually Edwin, and the Mimic (M2) killed him, as it has the same yellow eyes. There is even a tape in Secret of the Mimic that supports that M2 was in the room when Edwin died.
In FNAF World, everyone assumed 'Baby' meant 'Circus Baby', but I think he is actually referring to F10-NA (M1), as it is a common partner nickname (or too uncomfortable to say 'Fiona'). The dialogue even fits Edwin better, as he is under a lot of stress and pressure not to let his company fail, especially with investors like Fazbear's.
Edwin was actually the "mastermind" behind the mimics and was bought by Fazbear's. Henry was the design and technology lead at Fazbear's, but Edwin really implemented the technology at Murray's Costume Manor. (Edwin did not understand how M1 worked so well, but a theory is that it was through remnant from the Fall Fest fire, as stated in this comment.)
We see that there were debates about the character designs for the FNAF 1 pizzeria, as Henry was working with Edwin to implement the animatronics in a pizzeria.
While it is unclear which is the true ending of Secret of the Mimic, it is clear that Fazbear's eventually learned the science behind the mimics. By the events of the game, it is clear to Henry that Edwin (possibly his now good friend) has gone missing.
As Fazbear's now has access to Murray's Costume Manor and its technology, they now implement it in Sister Location. I believe FNAF 2 was Fazbear's attempt at new technology without this data (whether it happened before, during, or after Sister Location is unclear).
FNAF 2 and Sister Location could have also been Henry's way to honor his friend (or co-inventor at the least) by moving back to Fiona's costume designs and Murray's circus theme.
This would also explain why characters in Sister Location are more human-like and respond to human commands. It was essentially a research and development center. They could have been made with the metal infused with remnant from Murray's and implement Murray's technology. The higher intelligence of the mimics and human-like behavior was passed on to them. It would also explain why they are so much more robust and complex than animatronics at other locations.
Again, I am not sure whether FNAF 2 was around the same time as, before, or after Sister Location.