Rhystic Cave

• WWizards of the Coast2004-10-04
  Official Ruling
  Each player (starting with the current player and going in turn order) gets the option to pay when this ability resolves.
• WWizards of the Coast2004-10-04
  Official Ruling
  If a player pays , Rhystic Cave does not produce any mana, and is not considered to have been tapped for mana. Things which trigger of the land being tapped for mana will not trigger.
• WWizards of the Coast2004-10-04
  Official Ruling
  The card’s ability has errata so you can’t activate the ability during casting of a spell or activating of an ability. This prevents you from getting into a position where someone paying could stop you from having enough mana to pay for the spell. If you want to use it pay for a spell or ability, you need to use this card before you start the casting or activating.

Rulings via Scryfall