Yes they do become immortal, but that doen't mean they cant be truly killed.
A mortal ascending to daemonhood grants them immortality within the warp.
And as stated in the 8th edition of the core rulebook as you said.
The destruction of a Daemon's physsical form will banish it from realspace, but the malefic presence will gradually reform in the warp.
This is supported by the fact that Angron (a daemon primarch so once mortal) had been banished back to the warp.
Angron during the First war of armageddon.
However being immortal in this case does not mean they can't be killed.
This is called a True death this is when a daemons essence is utterly destroyed, this usually needs a special relic, ritual or psychic might.
This is what the Emperor did to Horus on the Vengeful spirit. But also what Kaldor Draigo did to kill a bloodthirster kalled Kar'Voth.
Some proof to this can be found in Chapter's due by Graham mcneil where the daemon M'Kar is shown to be given a true death.
The true mortal name of the daemon was said by Uriel Ventris and then stabbed by a powerfull relic by Marneus Calgar.
That had been Captain Ventanus’ last gift to Uriel: the true name of M’kar.
The daemon that had once been Maloq Kartho of the Word Bearers loosed a soul-hungry bellow and swept its clawed arms down to lift Marneus Calgar from the ground. Lord Calgar struggled in the grip of the daemon lord, but he was powerless to resist being drawn up towards its blazing fangs. Uriel saw the Thrice Born had cast off any notions of a grand victory here, and was contenting itself with the murder of the warrior who represented its most hated foes and had thwarted its insane ambitions for centuries.
Uriel snatched the flint-bladed dagger from the sheath at his side.
“I name thee Maloq Kartho!” he shouted. “Your true and mortal name!”
The daemon lord threw back its head in pain as a paroxysm of rage shook its body from the tip of its blackened horns to its splay-clawed feet. The dagger grew warm in Uriel’s hand, as though recognising a target for the lethal malice bound within its blade by unknown smiths of long ago. A shudder of unadulterated terror passed through the M’kar as it turned its gaze upon Uriel and saw the glinting dagger he carried. Its eyes widened in recognition. “The shard of Erebus!” cried the daemon lord.
As much as Uriel wanted to strike back at the daemon lord for all the suffering and death it had caused, he knew that was not the role fate had assigned him.
He was the Sentinel of the Tower, not its Master.
Uriel hurled the dagger, hilt-first, towards Marneus Calgar.
The Chapter Master caught it deftly, the slender weapon absurdly small in his mighty gauntlets. But just as the Gauntlets of Ultramar were capable of great destruction, so too were they capable of feats of great dexterity. Held less than a metre from the daemon lord’s face, Lord Calgar lunged forward and plunged the ancient dagger into M’kar’s throat.
The effects were instantaneous and incandescent.
After this it is described that the daemon suffered a true death and having its essence destroyed.
Blazing starfire spewed from the mortal wound dealt to the daemon lord, a flood of immaterial energy that raged in the air like a slick of polluted light. M’kar released its hold on Lord Calgar, who landed heavily on the ground before the dying daemon lord. Uriel ran to the wounded Chapter Master and, with the help of Pasanius and Learchus, dragged him away.
“What was that blade?” gasped Marneus Calgar.
“I do not know,” said Uriel. “It came from the tomb of Captain Ventanus.”
“Ventanus? The Lost Chapter?”
“The same,” confirmed Uriel.
The fighting in the valley had ceased as the daemon lord wrestled with its undoing, fighting with the last of its strength to withstand the alien sentience of the ancient dagger. Against the craft of its unknown makers and the revelation of its true name, there was nothing it could do, and every attempt to maintain its existence was for nothing.
All around them, the daemon host howled in mindless rage as M’kar drained them of their essences in its attempt to fight its own dissolution. One by one, the daemons disintegrated as their hold on the material world was broken and they were cast back into the warp. Within moments, the valley was empty save the for defenders of Castra Tanagra.
M’kar’s form shrank, its outline blurring and compressing as every shred of its existence was consigned to destruction. This was true death: oblivion and the terror of non-existence. And the daemon lord knew it. With a last shriek of terror, M’kar’s body exploded outwards in a wash of light scraps and horrified awareness of the nothingness that awaited it.