Generally speaking there may be a couple of issues here. As far as the "points" are considered, generally the State that issued the DL is in charge of assessing points to the Driver's license. For instance, I am an Arizona driver and if I get a ticket in California, AZ may assess points to my driver's license for the ticket. So, the CDL driver may get points.
Also, I believe CDL holders also have a national point system which builds points for different violations which can incur costs for insurance purposes.
Your driver should be ok but to be safe, call SOS Driver Services. They are the ones who load the driving records and send in reports to the fed government. Start at 217 524-1350. They ought to be able to steer you to the right place.
Definitely call the CDL help desk with the IL Secretary of State. I believe Mr. Harvatin provided that number in his response. They know all the ramifications of tickets both in and out of state. www.schaumburglegalservices.com