I played the Conjurer for the first time last night, and was confused about the "or an Action space" text. Your confusion is due to a misreading of the card. The text on the card is "Whenever you use the 'Traveling Players' action on an Action space, you receive one additional grain." So, anytime you use an Action Space that has the Traveling Players action, and you take that action, you get an additional grain.
I get that you get an extra grain for the Traveling Player space. What other spaces do you get the grain for?