That is not correct. It does replace regular swings with divine sacrifice swings.
The reason going from none to tier 1 gives such a huge boost is because you never reduced the DS intervall to 0. So it replaced the regular swings with 0 damage attacks.
Also, going from none to tier 1 will always yield more DPS than going from tier 1 to tier 2 or tier 2 to tier 3 because tier 1 gives a crit multiplier and 5d6 extra damage while the other 2 ranks just gives an additional 2d6 damage.