The activated ability doesn't change when you can cast the creature spell. In most cases, this means during your main phase while the stack is empty, although flash may change this.

Players can respond to the triggered ability that exiles the card from your graveyard by removing it in some other way. If the card leaves the graveyard before the ability of Serpent's Soul-Jar exiles it, Serpent's Soul-Jar won't let you cast it.