They're transparent about the mechanisms in general, but plenty of the mechanisms are arbitrary by nature. The article discusses hedonic adjustment for instance. That isn't a scientific or mathematical change. That's people at the fed making personal judgement calls about how good the iphone 12 is vs the iphone 11, and adjusting the price increases on the basis of that personal judgement call.

If you open the link you shared, you can see they make hedonic adjustments for men's suits, the first item in the list. Are suits today really much higher quality than they were 10 years ago, necessitating a decrease in the actual price inflation of a man's suit? The fed thinks so, but they don't share the details of why or how much hedonic adjustment men's suits deserve.