This may — or may not — be a consensus opinion, but here’s what I think:
When used as dormant spray, horticultural oil smothers insects coming out of hibernation. Its action is mechanical rather than toxic, so it needs to be applied while pests’ respiration is increasing — above about 40° F. The latest that such benefits are obtained is about 1/4-inch green, which can be a tolerably narrow window.
Concerning horticultural oil for control of codling moth:
I believe that apples universally reach full bloom at about 175 DD °F and that codling moths’ first flight (biofix) is about that time. Egg hatch begins around 425 DD °F (biofix + 250 DD °F), which is the traditional timing for first codling moth treatment. What the above article recommends is an early treatment at 375 DD °F to kill eggs before hatching. The author(s) suggest horticultural oil.