If you don't want to let your customers book a service on the current day, all you need to do is check "Disable same day booking" under your Service settings.
While the "Roundup starting interval" is added to the settings to enable same day booking.
Meaning the customer can book an appointment any time when is set to "Disable", or 15 or 30 minutes before the starting time.
A customer at 10h 45 am, can book a time slot on the same day at 11h00 am if you have 15 minutes on the settings.
Service > SAME DAY BOOKINGS