I did similar experiments with small amounts of dithionite added to dilute H2O2. This does not lead to formation of H2S, but it gives a turbid liquid, apparently containing finely divided sulphur.
Dithionite is very unstable in aqueous solutions and tends to disproportionate to thiosulfate and metabisulfite, which further react, giving all kinds of polythionates, sulfite, sulfides and sulphur. You get a really complex (and very smelly) mix of all kinds of oxo/sulphur ions. I indeed doubt that any H2S can survive when this mix is treated with H2O2, and so, I think that you might have used a low amount of H2O2, such that some remaining H2S could escape, before it is destroyed.
Besides that, I'm talking here about H2S, but is the smell of decomposing dithionite really from H2S. There may be small amounts of H2S, but I think that the main consituents of the evil-smelling cocktail are vapors of acids of the form H2SxOy and their decomposition products, with x and y having all kinds of integer values.
Try adding some neutral freshly prepared solution of dithionite to a dilute acidic solution. The liquid will turn nicely red, due to formation of hihgly colored species of the type H2SxOy.