Hm.  That's a little tricky, because the poison is in the neck, and if it's in the jugular, the jugular brings blood [i]back[/i] to the heart, so really the heart would be the first stop for the poison, then from there it gets distributed everywhere else.  But seeing how vampire transformations aren't instantaneous, it's probably a slow death for the heart.  It manages to distribute the poison for at least several moments before it dies, and considering the speed of the heart, a few moments is all it should take for full distribution.  I've also known of depictions of transformations where the heart beats faster at first before dying.

perhaps I'm overthinking this.  They're vampires.  What am I bringing so much science in for.

That's up to you, how long that thought process takes.