It's a tiny mistranslation. The Latin actually reads "in orbe (earth)". Hades is the underworld.
According to Ovid (“Metamorphoses” V, 551),the sirens were formerly handmaidens of Persephone, who at one point gets abducted by Hades.
Demeter then gives the sirens the bodies of birds, and sent them to the lower world (earth) to assist in the search of her daughter Persephone.
an quia, cum legeret vernos Proserpina flores, in comitum numero,
doctae Sirenes, eratis?
quam postquam toto frustra
quaesistis in orbe, protinus, et vestram sentirent aequora curam,
posse super fluctus alarum insistere remis optastis facilesque deos
habuistis et artus vidistis vestros subitis flavescere pennis.
But why have you, Sirens, skilled in song, daughters of Acheloüs, the
feathers and claws of birds, while still bearing human faces? Is it
because you were numbered among the companions, when Proserpine
gathered the flowers of Spring? When you had searched in vain for her
on land, you wanted, then, to cross the waves on beating wings, so
that the waters would also know of your trouble.
They eventually gave up and settled on the flowery island of Anthemoessa.