Sometimes on random days, I see Katrina's fortune-telling tent and ask her my fortune. But then the next day, her tent is gone. Does it spawn randomly, or does it have to have certain requirements to spawn?
Katrina's fortune-telling tent is one of a number of random visitors which may or may not arrive in your town each day (except Sundays, when Joan will always appear). There's no way to predict or control which character will visit on any particular day, except that no character will appear twice in the same week.
However, after having your fortune told 20 times by Katrina, she'll offer to let you build a permanent shop for her on Main Street as a Public Works Project.