1) First off, make sure that you have updated your iPhone to iOS 10.3 or later. With iOS 10.3, Apple fixed some problems with "background app refresh" that allow "auto sync" to work better than ever.
2) Don't force the app to close. This prevents the app from being eligible to run in the background.
- For more info on what it means to force the app to close, see: https://support.apple.com/en-us/HT201330
- It is the general consensus that forcing apps to close does not improve battery life as discussed in this articles:
3) Make sure that your iPhone connects to Wi-Fi when home, as auto sync is most likely to trigger when your phone is plugged in and connected to Wi-Fi.
4) Make sure that Low Power Mode is not enabled by going to your iPhone Settings > Battery
5) Make sure Background App Refresh is enabled by going to your iPhone Settings > General > Background App Refresh
Regarding the "Minimum Interval" setting, keep in mind that it determines the minimum time between syncs, but not the actual time. The app depends on iOS to wake up the app so that it can run periodically. The rate at which the app is woken up depends on a number of factors including whether your iPhone is connected to Wi-Fi, whether your phone is plugged in, how fully charged the battery is, and how often you use this app.