The Office Hours tab has a separate place to add your Online Hours that will show on your website.
Under Utilities - System Setup - General - Scheduler Settings - click the Office Hours tab - and you will see the Online Hours on the right.
The User Name must have the Role of Manager or Owner to be able to Change Online Hours.
Special Hours
Once you hit Update Online Hours it will take up to 24 hours to reflect the changes on the website.
Exceptions
To modify your hours when you are normally closed, only add the time frame you are adding availability instead of the whole day.
If you allow appointments for All Day for a half day change, then you will have a duplication of the office hours you are normally already open.