RNAi is a conserved mechanism in which small RNAs induce silencing of complementary targets. We have previously identified priRNAs, a class of Dicer-independent small RNAs in fission yeast. The mechanism by which Dicer-independent small RNAs are generated is not well understood in any species. Here we reconstitute the final steps of priRNA and siRNA biogenesis in vitro. We identify the 3'-5' exonuclease Triman and demonstrate that Argonaute, loaded with longer RNA precursors, recruits Triman to generate mature priRNAs and siRNAs. We show that priRNA and siRNA trimming is required for de novo assembly of heterochromatin at centromeric repeats and the mat locus and for maintenance of heterochromatin at developmental genes. Furthermore, in rrp6Δ cells RNAi targets diverse genes in a Triman-dependent way, indicating that the exosome protects the genome from spurious RNAi. Our results suggest that Argonaute association with RNA degradation products generates priRNAs and triggers RNAi in a process of transcriptome surveillance. 