Regulators of chromatin accessibility play key roles in cell fate transitions, triggering the onset of novel transcription programs as cells differentiate. In the Drosophila male germline stem cell lineage, tMAC, a master regulator of spermatocyte differentiation that binds thousands of loci, is required for local opening of chromatin, allowing activation of spermatocyte-specific promoters. Here we show that a cell type-specific surveillance system involving the multiple zinc finger protein Kmg and the pipsqueak domain protein Dany dampens transcriptional output from weak tMAC-dependent promoters and counteracts tMAC binding at thousands of additional cryptic promoters, thus preventing massive expression of aberrant protein-coding transcripts. ChIP-seq showed Kmg enriched at the tMAC-bound promoters that it repressed, consistent with direct action. In contrast, Kmg and Dany did not repress highly expressed tMAC-dependent genes, where they colocalized with their binding partner, the chromatin remodeler Mi-2 (NuRD), along the transcribed regions rather than at the promoter. We discuss a model where Kmg, together with Dany and Mi-2, dampens expression from weak or ectopic promoters while allowing robust transcription from highly expressed Aly-dependent genes.