Turnover of nucleoplasmic transcripts by the mammalian multi-subunit RNA exosome is mediated by two adaptors: the Nuclear EXosome Targeting (NEXT) complex and the Poly(A) tail eXosome Targeting (PAXT) connection. Functional analyses of NEXT and PAXT have largely utilized long-term factor depletion strategies, facilitating the appearance of indirect phenotypes. Here, we rapidly deplete NEXT, PAXT and core exosome components, uncovering the direct consequences of their acute losses. Generally, proteome changes are sparse and largely dominated by co-depletion of other exosome and adaptor subunits, reflecting possible subcomplex compositions. While parallel high-resolution 3′ end sequencing of newly synthesized RNA confirms previously established factor specificities, it concomitantly demonstrates an inflation of long-term depletion datasets by secondary effects. Most strikingly, a general intron degradation phenotype, observed in long-term NEXT depletion samples, is undetectable upon short-term depletion, which instead emphasizes NEXT targeting of snoRNA-hosting introns. Further analysis of these introns uncovers an unusual mode of core exosome-independent RNA decay. Our study highlights the accumulation of RNAs as an indirect result of long-term decay factor depletion, which we speculate is, at least partly, due to the exhaustion of alternative RNA decay pathways.