Turnover of nucleoplasmic transcripts by the 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 been based on long-term factor depletion strategies. Here, we rapidly deplete a NEXT, a PAXT and a core-exosome component, uncovering direct consequences of their losses. Global proteome analyses displayed only minor changes, yet exposed the immediate co-depletion of exosome and adaptor subunits, reflecting possible sub-complex compositions. Parallel high-resolution 3’end sequencing of newly synthesized RNA confirmed earlier established long-term depletion phenotypes. Still, rapid NEXT depletion displayed a narrower phenotype, illustrated by its restricted effect on snoRNA-hosting introns, whereas long-term NEXT depletion data had suggested a more general role of the complex in mediating intron turnover. While this validates snoRNA-hosting introns as primary NEXT targets, our data suggest that nuclear 5’-3’ RNA decay is altered after prolonged NEXT depletion, obscuring interpretation. Further analysis of snoRNA-hosting introns also uncovered an unusual mode of core exosome-independent RNA decay. Due to its non-processive nature, we speculate that this reflects a hitherto undisclosed exosome-independent activity of the EXOSC10 ribonuclease.