That's a good question.I have always assumed it was the second option you listed and played it as such but, I would be curious to know if anyone's been doing it differently and why.
We rolled 1 HD at lvl 1.Added +1 HP at lvl 2.Rolled another (1) HD at lvl 3 & added it to our total.Added +1 HP at lvl 4; etc...But it does cause confusion.
I think people have been debating this for nearly fourty years ;)I keep a cumulative total. I don't reroll the hit dice each level, although many OD&D players do, nor do I subtract the hit point from the previous level when getting a new hit dice. The way I play it, the +1 hit point every other level is like getting a new hit dice, but caps the hit points at 1.