The policy is that you can book on to any flight within 24 hours of your original departure. But you can only make the change within 12 hours of the new departure time.

In other words the agent was correct.

Assuming the 6pm "tomorrow" booked flight then starting at 6:01pm "today" the SDC window opens. From that time until the time of departure you are eligible to change to any flight that is departing within 12 hours of the "now" point that you try to make the change. So at 8pm "today" you can make a change to any flight between 8pm "today" and 8am "tomorrow." At midnight you have access to flights as late as noon.