Forming hydrogen sulfide from electrolysis of sodium thiosulfate
Yup, you're forming sulfide.

Render the thiosulfate ion as $(\ce {S-}-\ce {SO3-})$.  Then at the cathode:

$(\ce {S-}-\ce {SO3-})+2e^- \rightarrow \ce {S^{2-}}+\ce {SO3^{2-}}$

Both products are basic, with sulfide ion being strongly so,  and they will react further with protons; so the sulfide ion gives some hydrogen sulfide.  Sulfide ions can also combine with silver ions, from the anode, giving a black precipitate.  The other product, sulfite ion, can be reduced further, possibly forming still more sulfide ion/hydrogen sulfide.

So the reaction is not safe.  But kudos for using a fume hood.