In video, the monitor is the reference standard....... But the reference is an external target for the system that you do the color correction on.
That is the point. And all that has been debated in this thread turns arround this concept.
It could not be better resumed.
It's not colour managed but displays calibrated (if I can say it this way). So only if 2 displays have been calibrated the same way the video will match. This is why we see weired colours/gamma when doing a dcp in the sense that we rely on a standardized procedure that simulates the requirements for a targeted display (the projector) and ultimatly we have to check in situ (the theater) if what's been done was correct.
Experienced people mindset in motion is more like: ”I know 'this' is going to happen so I pre compensate doing 'that'.
Motion imagery crew are the best problem solvers on this planet.
And even so, there is no garantee that if you did everything right, your grade will match in every theater because the error factor may well come from the theater itself. And ultimatly...who did the calibration? In other words, even if you work on calibrated displays, how reliable is this calibration? And for what.
This is where people and companies like Shaw
https://www.lightillusion.com are important and those who have the knowledge
Are paied to bring order and maximize reliability.
I've got his downloadable software, it's not for everyone, it takes time and beyong the scope of my current habilities but also interests.
And this is also why you do not see one single image that matches your grade on a store tv showroom because none of those tv have been calibrated. Strong magenta, green shifts, uncorrect gamma etc...are the norm. Out the "security" of calibrated displays, it is the wild west.
Once your work goes out the bunker of calibrated displays, you can be sure that what you did will not be viewed like intended. So it's good you check on cellphones, the same way as high-end recording studios check their audios on low-end monitors to have an average idea of the audio experience for most consummers. (Prince was really good at that)
But also, as we are taking displays, we then can not ignore the viewing environment in which those operate. The amount of light in the room and other factors. The surrounding influences your colour decisions.
So if you don't know what you're doing wlth your displays and unless you are a crazy tech guru with 40 years of experience it's better not touching anything.
It's calibrated displays or the highway.