If the arrest was recent
Start with the county jail
Someone who was just arrested in Illinois is almost always in a COUNTY JAIL run by the county sheriff (or a city police lockup), not in a state prison, so the IDOC locator will not show them.
Illinois has 102 counties, each sheriff running its own jail with no single statewide jail roster.
Larger jurisdictions such as Cook County (Chicago) publish their own online inmate locator, but smaller counties may have nothing online.
The reliable paths for a recent arrest are the arresting county sheriff's jail roster, VINELink, or calling the jail's booking desk.
Illinois has 102 counties, each sheriff running its own jail; large counties like Cook (Chicago) post an online inmate locator while smaller ones may not, and there is no unified statewide county-jail search, so use VINELink or the arresting county sheriff.