When working in the week or month view of Daylite's calendar, you can display your appointments two different ways. By default, when you view your week or month view and click "today", Daylite will show you you're calendar looking forward rather then having your calendar start on a specific day.
If you prefer viewing your calendar so that the week/month starts on a Sunday, Monday et cetera, from within the General preferences for Daylite, you can toggle the "show week and month" to starting on first day. This way Daylite will respect your system preferences on your Mac.
Daylite General Preferences:
Mac System Preferences where you can set the day your calendar starts on: