The time zone is an hour wide. Solar noon and chronological noon cannot coincide with each other throughout an entire time zone.
I would say that Solar noon should occur some time in the noon hour. Solar noon should never occur prior to chronological noon, nor after the noon hour. Solar noon should never occur at 11:00am on the clock. Solar noon should never occur at 11:30am on the clock. Solar noon should never occur at 11:59am on the clock. Nobody should experience solar noon earlier than 12:00pm. Solar noon should be experienced sometime between 12:00pm and 12:59:59pm on the clock. Solar noon should be experienced within the noon hour.
The system that more closely aligns with this is Daylight Savings Time. Standard Time pushes solar noon forward into the morning hours for most people. DST keeps noon in the noon hour for most people. If you want chronological noon to coincide with solar noon, you need to choose DST, not standard time.