Yep, you've got it just about right, but the trigger percentages are in terms of remaining capacity, not in terms of sell-through. That is to say: an item might have a trigger at 30% for the Scheduled CAFs, meaning that it won't pull any of the item until the accumulator thinks the shelf is only 30% full (so for a shelf capacity of 30, it won't pull until the accumulator value or "need" reaches 21 (70%)). For the Autofill, though, the trigger will be higher--say, 60%, so it will pull some of the item if the accumulator value is at 12 (40%) or more, because it's easier to pull and stock things during the Autofill process (and it increases the number of items that will start the day with a full shelf). And for a manual CAF, unless things have changed since I left, there are no trigger percentages. It should pull any item that has a backroom location and a non-zero accumulator value--this is why manual CAFs sometimes pull things that don't even have sales floor locations (or, again, at least they used to).
As to consistency throughout the day, I was never aware of any triggers that changed from one CAF to the next, though it certainly wouldn't be impossible to set the system up that way. It might even make sense--you might leave a low trigger for the 11am-2pm batches, letting the shelf get a bit emptier when there's nobody shopping anway, but set the triggers higher (meaning it pulls the item after fewer units have sold) for the 3pm-5pm batches in order to keep the shelves looking extra full and impactful during the hours people actually shop.
And as to why they'd be increased, well, that's just an extension of the last point--it keeps the shelves closer to full at all times, which improves the presentation/brand. You'll pull the item more often, but fewer of it each time; apparently HQ has decided that for your store, the extra work will be justified by the improved appearance.