Okay guys, I'm going to attempt something incredibly ambitious, and that is to piece everything together about this series. It may seem like Emil Macko left the series unfinished, but in reality he has tied up every single loose end and completely explained the lore.
[MASSIVE SPOILERS AHEAD, PLAY ALL THREE GAMES TO COMPLETION BEFORE READING]
Now, in order for any of this to make sense, I am going to point out Emil Macko's use of symbolism. This game is not meant to be interpreted literally, as some parts of the original FNAF series are. For example, Monster RAT and Monster CAT are explicitly stated to be "nightmares". That means that what you are seeing isn't necessarily real. But it isn't fake, it simply is a representation for something else.
With that in mind, let's take a look at what happens during the cutscenes of FNAC 1. You look around on a singular camera and stuff starts to happen, particularly Vinnie roaming around near the assembly line. But what if I told you that even though you see Vinnie during these cutscenes, he's actually a representation for something else? Ladies and gentleman, I believe that the person who was really roaming around the factory that night was...
In case you haven't played the game and waltzed past the spoiler warning, or just need a refresher, The Puppeteer appears during Mary's flashbacks to The Rat & Cat theater. He is the actor in charge of controlling Vinnie and the eventual murderer of the two employees in the Rat and Cat costumes. Now, him shoving Rat, I don't blame. Rat was trying to choke The Puppeteer to death. I would probably have reacted the same way. Then, the actor wearing the Cat costume shows up. He tries to call the police, but fearful of getting caught, the Puppeteer garrottes him with some wire. He then calls the police himself, saying he found them dead.
Later on, the Puppeteer is found out when Mary's psychiatrist calls the cops in light of her information. This presumably gets the Puppeteer thrown in jail, as shown by Vinnie's dialogue before the Final Night. The way I interpreted this is that the Puppeteer, angry at Mary, breaks into her house and attempts to kill her. He is unsuccessful, but that doesn't mean that he will give up so easily.