In my department, not all members of the SC are at the conference interviews. So the full SC has to meet, and those who were at the conference interviews will explain which handful of people (about 6 out of 12 to 15 interviewed, to be winnowed down to 2 or 3) ought to be considered for a campus visit. Then (at least in my experience), there is a big fight because those who did not go to the conference but who "fell in love" with a candidate on paper can't comprehend that a person can fall flat in person. After hours of fighting, the SC finally comes up with the list. At my uni, that list has to be approved by the Dean's office, but that's more a case of the Dean approving the funding for those visits, not the candidates themselves. This process, at my university, takes about a month to 6 weeks. Most other places make the call within about 2 weeks of the conference.
However, our Dean once dipped into our stack of applicants and insisted that we bring an additional person to campus.
My Big State U is similar to the process onion describes but first the committee returns, meets and ranks the AHA interviewees, then they wait for the faculty to return from break so they can be told that the SC likes X, Y, and Z for on-campus visits. About a week after faculty returns and has a chance to review the 10 AHA files and compare them to the 3 finalists of the group the SC picked, we meet as a faculty to second guess the SC! Well, sometimes, often its rubber stamp the SC once they explain that "Mr. Looks Fab on Paper" picked his nose and ranted about the Gold Standard like an 80 year old man at his AHA interview, so, no, the SC doesn't want to see *him* again thanks!
Once the faculty votes to bring X, Y, and Z to campus, the chair contacts the Dean to release the funds and travel arrangements are made! Usually its by the 20th of January in my place. I have known many, esp those dealing with private Us and SLACs who have gotten calls within days of AHA. Depends on who has to approve the choices, what has to be done to get money released, and even what the schedule is for visits---in years with several searches, one might not get "moved" on in my dept until 3 weeks after the conference.
You never know, everything is different at each institution.