So the best answer to this question, I think, is like you already said, every school is different. Usually how it goes is that the person who you specified in your graduate application and on your personal statement (your POI - Professor of Interest) will have a large say in who they want to interview for their specific lab - makes sense, right, because they are going to be the ones that you work the most closely with over your 5-6 years in the program.
Anyway, the university as a whole has to send a large stack of applications to the psych department and then these applications get sorted and sent to the specific POI's within the department who then sort through the piles and pick the best applicants to call and make interview offers too (or sometimes pre-phone interviews).
So the reason that this doesn't usually happen until mid January is because most professor have winter break, and thus, are doing other non-academic things. I would say that it is pretty rare actually for faculty to notify people so early (i.e. mid-December). Main take away: Don't freak out, this is totally normal not to have hear from places yet.
Some faculty are just really just ahead of the pack and like to do things early. Others like to wait until after the holiday to do this. If you applied to one of these schools above, that doesn't necessarily mean that you didn't get an interview there. Right, because maybe only one professor at University of XYZ has sent out interviews yet. From my own experiences and from knowning a lot of people who are applying this year, I know this is the case at several schools above actually.
So in conclusion, don't give up hope. It's still wicked early.
