According to Wikipedia (https://en.m.wikipedia.org/wiki/House_of_the_Vettii) the House of the Vettii brothers had two atria, one specifically for slaves.
Servants' quarters are to one side off the atrium, arranged round a small atrium of their own.
However, according to this discussion of the house, http://web.mit.edu/course/21/21h.405/www/vettii/houseblue.html the room identified as the slave's atrium is a courtyard, with a compluvium -
Room v is in the northern corner of the house. From the room, also considered a courtyard, a variety of other rooms can be accessed. To the west, the room leads to room w. Room x and y are off of the northern corner of the room. Room z also has a small entranceway to the northeast, as does room 08 which is off of the eastern corner of the room. In the center of the room is an impluvium, or pool. On the western wall there is a painting of lararium aedicula (seen in the photo). The painting was done in Fourth Style. Artifacts found in the area, such as razors and cups, suggest the room served a bathing purpose. emphases mine.
Against this, the "slaves' atrium" does appear to lead to the kitchen, and is largely separate from the reception areas of the house. Moreover, in Rome:Its People, Life and Customs, U E Paoli (1958) states that in The House of Pansa,
"There are two adjoining atria.... the Tuscanicum and it's surrounding rooms were used by the owner's family. The tetrastyle, on the other hand,... was in the humblest part of the house, reserved for slaves." p68
In my admittedly limited understanding, the notion of specific "servants' quarters" - particularly an atrium - seems anachronistic; according to some ancient writers, slaves should be either working or sleeping, so why would they need an atrium? I have always understood that Romans shoehorned their slaves in wherever there was space, and the notion of providing a room for their own use appears unlikely. I realise history is not linear, but servants' quarters in the sense of the great country houses was a fairly late development; medieval servants bedded down wherever they could!
Can anyone resolve my confusion?