The automatic night theme is reliant on your iPhone having auto brightness turned on in your main iPhone settings.
If you go to your iPhone's Settings, pull down to see the search bar and enter 'Auto Brightness', tap on the result labelled 'Auto-Brightness'. You should see a switch for Auto Brightness at the bottom of the screen that you should toggle off and back on. This is normally all that is needed to fix automatic switching to the night theme.
Another reason for the night theme not being switched to automatically is that it might not be dark enough to trigger. If your in a dark room and want it on but its not switch on automatically, go the the settings screen in Baby feed Timer and drag the slider for 'Automatic night theme' towards the right a little and then back out of settings to test. The further the slider is moved to the right the less dark the room needs to be to switch to the night theme.