If the difficulty scaling is the same as in BotW, then the time silver monsters pop up depends solely on the amount and type of enemies you've defeated. Think of it as an reverse XP-based system; strong foes are worth a lot of XP, weak foes are worth less. If you kill a lot of "big" monsters, you ramp up a lot of XP, and eventually the monsters scale up to stronger variants.

The amount of shrines, temples, the Master Sword, heart containers or anything regarding the story / quests was completely irrelevant in BotW, so I'd wager it is the same for TotK.