He is seen leaving the palace and heading outside.

As for the TDR scene, it's vague since we don't know exactly where they entered TAR or how they left TAR (it's clearly not Traveling since Rand magically reappears without making a Gateway).

TDR
What is written in Prophesy

And then he was in the Heart of the Stone again, stalking through the rubbled gap that had been a wall. Some of the columns hung like broken teeth, now. And Ba'alzamon backed away from him, eyes burning, shadow cloaking him. Black lines like steel wires seemed to run off from Ba'alzamon into the darkness mounding around him, vanishing into unimaginable heights and distances within that blackness.

"I will not be undone!" Ba'alzamon cried. His mouth was fire; his shriek echoed among the columns. "I cannot be defeated! Aid me!" Some of the darkness shrouding him drifted into his hands, formed into a ball so black it seemed to soak up even the light of Callandor. Sudden triumph blazed in the flames of his eyes.

"You are destroyed!" Rand shouted. Callandor spun in his hands. Its light roiled the darkness, severed the steel-black lines around Ba'alzamon, and Ba'alzamon convulsed. As if there were two of him he seemed to dwindle and grow larger at the same time. "You are undone!" Rand plunged the shining blade into Ba'alzamon's chest.

Ba'alzamon screamed, and the fires of his face flared wildly. "Fool!" he howled. "The Great Lord of the Dark can never be defeated!"

Rand pulled Callandor's blade free as Ba'alzamon's body sagged and began to fall, the shadow around him vanishing.

And suddenly Rand was in another Heart of the Stone, surrounded by columns still whole, and fighting men screaming and dying, veiled men and men in breastplates and helmets. Moiraine still lay crumpled at the base of a redstone column. And at Rand's feet lay the body of a man, sprawled on its back with a hole burned through the chest. He might have been a handsome man in his middle years, except that where his eyes and mouth should have been were only pits from which rose tendrils of black smoke.