I can't live without TrueTone anymore. It is so much easier on my eyes to not have glaring white balance issues any more.
Your eyes get used to it. We are incredibly good at adjusting our mental white balance to our environment so that white always appears white to us. When you turn it on and off the shift in color is obvious, but once it's left on and you stop paying attention TrueTone should feel more natural.
There are two different systems that both play with the white balance of your display: True Tone and Night Shift. True Tone is meant to make your screen behave like paper does-- it makes white look like the ambient light in the room. Night Shift is different, it intentionally inhibits the blue to minimize sleep disruption. True tone should look natural for the room, Night Shift will make the display look warmer than its environment.
White surfaces reflect the light in the room. If you're in a room with a window, the light in the room is warmer (more yellow) at sunrise, then gets quite cold (bluer) as the day goes on particularly if the direct sunlight is blocked, then warmer again at sunset, and then takes on the color of your artificial lighting (warm white, cool white, etc). A truly white sheet of paper will be the same color as the light.
Have you ever noticed when you walk down a street at night that the rooms with TVs on all look blue? But when you're in a room watching TV it doesn't look blue at all? The TV doesn't care what time of day it is for you, it's presenting an image of the time of day in the movie and if it's daytime in the movie the image is cooler, and more blue. When you're in the room your eyes are adapted to the big TV and white on the TV looks white. If you're in the street your eyes have adapted to warmer artificial lighting and the white from the TV looks blue.
Same if you've ever taken a film photograph indoors without flash-- you'll get the photo printed and take it home some afternoon to look at and it looks yellow. It didn't feel yellow when you took the photo because your eyes were adjusted to the warm artificial light and white in the room looked white at the time. But now you're in cooler indirect sunlight and your eyes are adapted to it so the warmer light the film caught accurately looks yellow to your brain. Digital cameras tend to correct for this at least a bit, but film captured what film saw.
True Tone measures the light in the room and makes white on the screen match the color of that light so that it behaves more like paper would. With True Tone off, a white screen probably looks a bit cold and blue in a room at night, with it on it should more closely match everything else that's white. Turning it on and off your eyes will see the change, but if left on it should blend. There's some situations that can upset the system (if the sensor is looking at light that isn't truly ambient, for example sometimes I cover my Macbook camera with a yellow sticky note and that shifts the display color).
Night Shift is different, night shift pushes the color temp warmer than ambient specifically to reduce the blue in the image because blue disrupts melatonin. As melatonin accumulates in your body, it tells your body to sleep. In the morning the light (most specifically the blue light) breaks down the melatonin and you start to wake up. Blue light from screens can disrupt that melatonin production and impact your sleep cycle, so turning the blue light down helps (a bit). Since it's warmer than ambient though, your eyes will more easily perceive small screens as yellow in this case.