After you switch from Daylite to another app on the iPhone & iPad, it will continue to run for short period of time before it is put into a suspended state by iOS. In a suspended state, Daylite on the iPhone & iPad isn't actively in use, open, or taking up system resources.
With Background App Refresh, Daylite can check for updates and new content. When Background App Refresh updates Daylite is determined by iOS, and is based on many factors like frequency of updates, location and battery levels.
If you want suspended apps to check for new content, go to iOS Settings > General > Background App Refresh and turn on Background App Refresh. If you quit an app from the app switcher, it might not be able to run or check for new content before you open it again.