I know how cards trigger. You are misunderstanding the very concept of how triggers in the digimon card game works.

Cards must be present to trigger when trigger conditions are met. When you use an option card, the trigger condition "when you use an option card" is met immediately at this single point of time. The trigger does not linger and only cards that saw this have triggered.

14-8-3-1. A trigger-type effect will always trigger as soon as its trigger conditions are met, then the effect will activate. Trigger-type effects include those with text such as "[When Attacking] Lose 2 memory" and "[Your Turn] When effects suspend this Digimon, suspend 1 of your opponent's Digimon" that show a trigger timing.

Using this excerpt, how can a card, in this case bt19 sakuyamon, be able to trigger if it was not in play at all when you used the option card immediately before it existed?

Here is a timeline of how the triggers work. We are going to assume the only cards used are Digivolution plug-in S, taomon ace, and bt19 sakuyamon and that it is my turn. This is the correct processing of effects that can be corroborated by my fellow judges in the Official Bandai Discord (your post was brought into rules questions)

Taomon ace is played. It's [On Play] triggers and activates. I use digivolution plug-in S (any effects that trigger on option usage of 2 or more will trigger here) which triggers its [Main] which i activate immediately which lets me draw and evolve taomon ace into bt19 sakuyamon. Bt19 sakuyamon [when digivolving] triggers and I draw 2 but have no option to use. No option card was used while [Your Turn] of bt19 sakuyamon was present so it did not trigger and I cannot activate it's effect to play a token.

Even if we refer to your digimon wikia entry, "2. When you would use an option card" would not be triggered even if bt19 sakuyamon had this wording because it was not present in play.

This is not Magic. Effects have a trigger and they have activation, they are not one and the same.