Could also be a sort of subtle nudge to a characteristic of Andrea's character throughout the play. Something about a disconnect or loss of identity that haunts him or influences the ways he behaves.

In the context of Elizabethan England it feels sort of telling that his soul immediately descended upon death. Even with the overall story's themes of Greek/Roman mythology the audience would have been immediately familiar with the Christian undertones akin to Dante's Inferno. It feels intentional to mention this as it would make audience members assume something about his character being immoral or bad in some way.