Once a person is arrested and taken to jail it can take up to 2 hours for the inmate to be put into the system after being booked.
Sometimes it can take 30 minutes or so before the inmate is actually processed and booked into the jail officially depending on how many more inmates the jail has to book that day.
So it can take from 1 to 2 hours for the inmate to show up on the inmate search for the jail.
For prison it can take 1 to 2 days for the inmate to show up in the system so even if a prisoner arrives at prison to start their sentence it can take 2 days before you're able to locate the prisoners information on the inmate search website.
Sometimes it happens sooner but sometimes it takes a bit longer for the information of the inmate to be put into the system depending on how busy the jail or prison is.
The inmates information and picture is added to the system manually in most cases.