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 -> Display & Brightness and toggle 'Auto-Brightness' off and back on can normally 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.