Yes. Your interpretation is correct.
I have not recently read the sutta. But it is likely that Chieftain Pāyāsi believed in a soul and he wanted to see a soul coming out of a dying person.
If a human dies and there is more kammic energy left in the human bhava, then the gandhabba would come out. Of course, even then that gandhabba cannot be seen by the naked eye.
– If that human was at the end of human bhava, then nothing will come out of the dead body if that human is reborn as a Deva or Brahma. In that case, a Deva or Brahma will be born in the appropriate Deva or Brahma realm simultaneous with the death of the human.
– If rebirth is in the animal realm, then an animal gandhabba will come out of that dead human body.