Cico trusts Tony because of a feeling he has; he instinctively senses that Tony is someone who will be receptive to new spiritual experiences. In Chapter 11, when Tony demands to know why Cico trusts him with the story of the golden carp, Cico contends that there are no rules on who he can choose to trust with the story. He merely trusts those he knows will understand and appreciate the significance of what he's telling them.
Later in the chapter, after Tony catches a glimpse of the magnificent golden carp (it is bigger than Tony himself), Cico maintains that only those who believe can see the carp. In fact, Cico asserts that many fishermen who fish at the pond can't see the carp themselves. The implication is that these fishermen aren't receptive to things they can't understand. Upon hearing Cico's words, Tony feels as if he belongs to a group of very special people.
Cico also tells Tony that the carp will eventually swim to the Hidden Lakes in the hills; the lakes are rumored to have no bottom. Cico also warns Tony against going to the Hidden Lakes alone. Accordingly, a shepherd had once been lost at the lakes, and the rumor is that a strange magic permeates the lake area.
Cico also acquaints Tony with the prophecy of the golden carp. According to Cico, the golden carp will come to rule the world after all the sinners are drowned. The golden carp has apparently proclaimed that, if the people continue in their sins, the whole town will collapse and be swallowed up by the waters of the lake. For his part, Tony feels ambivalent about the prophecy. While he thinks that the prophecy sounds plausible, he wonders how anyone can avoid sinning, especially since Cico assures him that "all men sin."
However, Tony never displays any sort of outward skepticism about the prophecy or the golden carp; this is probably the main reason that Cico trusts him with the story.