When you answer a call and put your phone to your ear, the display is intended to go black so you don't press buttons onscreen with your face while you're talking. But if it goes black before then, I am more likely to think this is an issue with the proximity sensor. It could be that the phone thinks it is close to your face, even when it's not.
True Tone is to some extent also related to sensors on the same cable, specifically the ambient light sensor, but I would look into replacing the front facing sensor cable. Be aware that this will disable Face ID unless the components that are tied to Face ID are moved over to the new cable since that's where the sensor for proximity lives.
A little history of the device may help the specifics (why doesn't it have the original screen, what happened that it needed to be replaced?)
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