I think you may be confusing three different issues. The first issue is that there was a piece of Voldemort's soul inside of Harry. The existence of that piece of soul tethered Voldemort to life – he could not be killed as long as Harry remained alive. That was taken care of when Voldemort "killed" Harry in the Forbidden Forest. At that moment Voldemort actually killed the portion of his own soul that was housed in Harry, thus leaving himself open to being subsequently killed.
Then there was a separate tether that kept Harry alive as long as Voldemort remained alive. This was because Voldemort regenerated his body using Harry's blood. Therefore while Harry's blood still flowed in Voldemort's veins, Harry could not be killed. This was explained in Chapter Thirty-Five of Deathly Hallows:
“But if Voldemort used the Killing Curse,” Harry started again, “and nobody died for me this time – how can I be alive?”
“I think you know,” said Dumbledore. “Think back. Remember what he did, in his ignorance, in his greed and his cruelty.”
Harry thought. He let his gaze drift over his surroundings. If it was indeed a palace in which they sat, it was an odd one, with chairs set in little rows and bits of railing here and there, and still, he and Dumbledore and the stunted creatures under the chair were the only beings there. Then the answer rose to his lips easily, without effort.
“He took my blood,” said Harry.
“Precisely!” said Dumbledore. “He took your blood and rebuilt his living body with it! Your blood in his veins, Harry, Lily’s protection inside both of you! He tethered you to life while he lives!”
When Harry and Voldemort face off again shortly thereafter, Voldemort is still alive. This presumably means that Harry still cannot be killed, since his blood inside Voldemort would still be tethering him to life. However, there is nothing to indicate that this "tether" can cause a curse to rebound. Indeed, when Voldemort tried to kill Harry in the forest the curse did not rebound.
The original rebounding curse when Harry was a baby was caused by something else. In that instance the curse was deflected by Harry's mother's sacrifice. Her love acted as a shield, thus deflecting the curse back at Voldemort. However, that particular protection had been overcome by Voldemort in Goblet of Fire when he used Harry's blood to regenerate himself. As he said then:
"His mother left upon him the traces of her sacrifice.... This is old magic, I should have remembered it, I was foolish to overlook it... but no matter. I can touch him now."
Harry felt the cold tip of the long white finger touch him, and thought his head would burst with the pain. Voldemort laughed softly in his ear, then took the finger away and continued addressing the Death Eaters.
This was also confirmed by Dumbledore that same night:
"He said my blood would make him stronger than if he'd used someone else's," Harry told Dumbledore. "He said the protection my – my mother left in me – he'd have it too. And he was right – he could touch me without hurting himself, he touched my face."
For a fleeting instant, Harry thought he saw a gleam of something like triumph in Dumbledore's eyes. But next second. Harry was sure he had imagined it, for when Dumbledore had returned to his seat behind the desk, he looked as old and weary as Harry had ever seen him.
"Very well," he said, sitting down again. "Voldemort has overcome that particular barrier. Harry, continue, please."
Therefore, without the Elder Wand factor in the final duel, Voldemort would probably not have been killed. If Harry had let himself be hit with the Killing Curse, he probably wouldn't have died since his blood in Voldemort still tethered him to life, but since the original protection from his mother's sacrifice was no longer operational the curse would probably not have rebounded at Voldemort either. Therefore Harry needed Expelliarmus to cause Voldemort's curse to rebound.