When you use the Type a task field in the To-do bar, the due date is set automatically for you, picked up from the Quick Click flag setting.
The reminder time is based on the Quick Flag - Today flags have reminders set for one hour before the end of your work day as set in Calendar Options. (For most people, the reminder is 4 pm.) Tomorrow, This week, or next week use the reminder time as set in Options, Task Options.
If the option to disable reminders on task with due date, then no reminder is set.