What the human studies tested
Gooley and colleagues compared room light with dim light before bedtime in healthy young adults. Room light delayed melatonin onset and shortened its duration under those laboratory conditions. The experiment concerned overall light exposure, not Tap Zap or a particular red-screen setting. Read the 2011 study.
Chang and colleagues compared evening reading on a light-emitting eReader with a printed book. The eReader condition affected melatonin, circadian timing, sleep, and next-morning alertness in that controlled experiment. It did not test whether a screen filter prevents those effects. Read the 2015 study.
A software setting is not an optical measurement
Tap Zap changes requested RGB values using display transfer tables on Mac, a color matrix through the Magnification API by default on Windows, or gamma ramps in Windows Legacy Mode. Its strongest warmth setting sets the requested green and blue channels to zero. The label 0K names that software setting; it is not a physical color temperature. The spectrum emitted by a panel depends on its primaries, profile, and active mode. A red appearance or screenshot cannot establish zero blue optical output.
These studies support taking evening light exposure seriously. They do not establish a clinically effective Tap Zap setting, a universal safe spectrum, or a guaranteed sleep outcome.