When working in the week or month view of Daylite's Calendar, you can display your Appointments two different ways.
By default, when you're in the week or month view, and click "today", Daylite will show you your Calendar looking forward rather than having your Calendar start on a specific day.
If you prefer viewing your Calendar so that the week/month starts on a Sunday, Monday, etc, from within the Calendar 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 Calendar Preferences:
Mac System Preferences: where you can set the day your calendar starts on: