It might be as soon as a few hours, but it could also take a couple of weeks. There are variables that could make either scenario true, we just don't have enough information. For instance, was the inmate transferred within a similar system? If so, it might be no time at all. If it's a new system, then there is an A & O period that would make it many days before phone lists are able to be updated.
https://www.inmateaid.com/ask-the-inmate/how-long-will-it-take-for-my-inmate-to-call-me-after-a-transfer#answer
Accepted Answer Date Created: May 03,2016