Does Rhystic Study trigger if an opponent pays the one mana before casting their spell rather than as an additional cost?

Rhystic Study reads: "Whenever an opponent casts a spell, you may draw a card unless that player pays {1}." The triggered ability checks whether the opponent pays {1} as part of casting that spell — specifically as an additional cost during the casting process defined in CR 601.2.

Paying mana before a spell is cast (e.g., floating mana in your pool ahead of time) has no bearing on whether the Rhystic Study payment is made. The payment of {1} must happen during the spell's casting, as the additional cost Rhystic Study imposes. It is not a separate, pre-cast transaction that can satisfy the trigger's condition (CR 603.5, 118.9).

In practice, when Rhystic Study's ability triggers (upon an opponent casting a spell), the opponent is given the opportunity to pay {1} at that point. If they choose not to pay — regardless of what mana they had or spent earlier — you draw a card. There is no mechanic by which paying mana before a spell is cast can satisfy an additional cost imposed during that spell's casting.

Example: Your opponent has {U}{U}{1} in their mana pool from tapping lands before announcing a spell. When they cast Counterspell, Rhystic Study triggers. They must still pay an additional {1} during that casting to stop you from drawing. The mana they floated earlier doesn't automatically count as that payment.