You are correct that your home state of Illinois as well as Texas are part of the Drivers License Compact (DLC) which means that their courts and Department of Motor Vehicles exchange information in regards to drivers who receive moving violations out of state.

Both states are also members of the Non-Resident Violator Compact (NRVC) which is what allows your home state to suspend your driver's license if you do not pay or otherwise take care of the out of state (Texas) ticket, not the the DLC.

Whether a ticket or violation will show up on your home state's driving record or be assigned points is up each individual state's laws and statutes. The drivers section of the IL Secretary of State site does not mention specifically that out of state tickets are put on your driving record. However the Illinois Administrative Code Motor Vehicle gives information on the Illinois offense table. Here it notes that all out-of-state convictions are to be considered and to be coded exactly as Illinois Vehicle Code violations with the exception of the first digit which shall be an “8.”