Soap doesn't come with a specific time table for when it's ready to cut. It is ready when it's sufficiently but not overly firm. If you make a particular recipe several times, you'll gain experience to know when it's ready, but if you're making recipes new to you, you will need to check the soap for the right firmness. In some cases, yes, you might need to cut when the soap is still warm. But again the correct firmness is the key criteria, not temperature and not time.
Here are some analogies based on cheese -- Soap is ready to cut when the soap is firm yet yields slightly to the touch, similar to refrigerator-cold colby or mild cheddar cheese. If it feels soft and can be dented easily -- like cold cream cheese or brie -- you need to wait. If it feels very hard like aged cheddar or Parmesan, you might be too late.