You’re not overthinking it, timing does matter a little, just not in a dramatic way.
I add mine in the evening most of the time, mainly because it’s more efficient. UV absolutely breaks down free chlorine, especially if your CYA is on the lower side. If I add 3 to 4 ppm at noon in July, I can watch a chunk of that disappear by late afternoon. Add the same dose after sunset and it gets a full night to oxidize organics before the sun starts chewing on it.
That said, daytime dosing isn’t “wrong.” If your stabilizer is in range and your daily chlorine loss is predictable, it’ll still work. I’ve added during the day plenty of times when I’m adjusting after testing. The key is knowing your pool’s demand. My pool in 85 degree water with a decent bather load will lose more than 2 ppm on a sunny day no matter what.
What made it click for me was tracking daily loss for a week. Once I knew roughly how much I lose to UV versus actual demand, the timing question felt less mysterious. Evening just stretches your chlorine’s efficiency a bit. It’s not magic, just less sun fighting it right away.