Another reason may be that location services is turned off.
Apparently, in that case, the system gets the time for sunrise and sunset wrong.
I just experienced this: it was well after sunset, I toggled Night Light on. Nothing happened. Schedule was set to "Sunset to Sunrise", as desired. Then I moved the Color Temperature slider and the screen's color immediately changed. But after a few seconds, it just changed back.
I didn't have Redshift installed in the first place.
But when I enabled Location Services (Settings → Privacy → Location Services) the Night Light kicked in almost immediately. And stayed on.
So, this seems to be another possible cause for the symptom described in the original post.