I have trouble with this, too. If a planet is tidally locked, it would get searing hot at the point that has the most direct sun, and freezing cold on the back. Although atmospheric winds would moderate this somewhat, I can’t see a situation where life would take hold without any sort of day-night cycle or where the sun never moves in the sky.
Around the terminatior there would be a “seasonal” variation of night vs. day, the significance of which would depend on the tilt of the planet’s axis. There could be significant, predictable movement of the termiator at hihger lattitudes.