I installed and configured your Appointments+.
I inserted as Time Base 15 and configured work time from 9:15 to 19:00 with a break from 12:30 to 16:15.
My services are of 30' and 60'.
If I select a service of 30' first time slot is 9:30-10:00 and not 9:15 because calendar show slot as 9:00 - 9:30 unavailable.
If I select a service of 60' first time slot is 10:00-11:00 and not 9:15-10:15 because calendar show slot as 9:00 - 10:00 unavailable.
Same problem with afternoon start time, appointments never starts at 16:15 and user can't select a quarter of an hour (in example, if it's free set an appointment to start from 18:15).