Specifically it mentions battles being fought to the north and it mentions Galadriel bringing down the ancient fortress of Dol Guldur up in Mirkwood (where Sauron had hidden out as 'the Necromancer' before relocating to Barad Dur in Mordor).
This happened between LOTR and the Hobbit. BTW
Of all the Istari, Gandalf was most interested in the world of man. Most of the others failed or did not do their duty.
Of these five, only Gandalf remained true to his purpose, for Alatar and Pallando were gone into the east, and Radagast paid no heed to the darkness, and Saruman himself became enslaved by the Enemy. For he, after settling in Orthanc, found one of the Palantíri of Fëanor, of which the men of Númenor had been given, and so were brought into Gondor and Arnor by those faithful of Númenor. But now Saruman gazed into that seeing stone of Orthanc, which may have been forgotten when he was given the keys, or held of little value to the Stewards any more than an heirloom, and was ensnared by Sauron, who also had obtained the stone of Minas Ithil, by turning the Orthanc-stone to his, and turned Saruman to evil. For Saruman was the most knowledgeable of the White Council in ring-lore, and he began to search now himself for the One Ring of power, for he wanted to become a Power himself, and rule over Middle-earth in Sauron's place. And he it was who bred orcs with Men and played many other foul parts in the War of the Ring, pressing the Men of Rohan and destroying their sons. But he was ousted, by the Sheperds of the Trees, the Ents, who he had forgotten, for his orcs destroyed their forests and their flocks of trees, and so they came against him, unseen, and they destroyed Isengard, and his army. Afterwards he retreated to the Shire, which he befouled, and was there slain by his twisted servant, and was never seen again. In Orthanc was found the Elendilmir which was lost with Isildur, and so it is guessed that Saruman found the remains which brings into thought terrible things, for who knows what Saruman may have done with Isildur's remains if he did find them?
But Gandalf remained true, as has been said, for his work ever drove the Children against Sauron, who was defeated and vanquished, and so Gandalf alone of the Istari returned to the West with the Ringbearers whom he had loved, most of all the Halflings of the Shire. He it was who took most notice of the Shire and the Hobbits, and he smoked like they did but perfected it and he loved the little people. It was this love that brought him into the friendship of Bilbo Baggins of Bag End who found the One Ring, and so the Ring was destroyed by Bilbo's heir, and Sauron perished.
These should answer any further questions
The movies are entertaining but they take quite a few liberties especially in the Hobbit ones, those do not even resemble Tolkien's work at times and are Hollywood.
The excerpt you posted is contradicted by Tolkien himself. And Tolkien is contracted by Tolkien himself.
Early on, Tolkien said of the Blue Wizards, "I really do not know anything clearly about the other two [wizards] – since they do not concern the history of the N[orth].W[est]. I think they went as emissaries to distant regions, East and South, far out of Númenórean range: missionaries to 'enemy-occupied' lands, as it were. What success they had I do not know; but I fear that they failed, as Saruman did, though doubtless in different ways; and I suspect they were founders or beginners of secret cults and 'magic' traditions that outlasted the fall of Sauron."
And he claimed that of all 5, only Gandalf returned to Valinor:Wilt thou learn the lore || that was long secret
of the Five that came || from a far country?
One only returned. || Others never again
But later in his life, Tolkien re-thought of their fate. He gave them different names (Morinehtar and Rómestámo) and in his last writings said, ""But the other two Istari were sent for a different purpose. Morinethar and Rómestámo ( Darkness-slayer and East-helper ) Their task was to circumvent Sauron : to bring help to the few tribes of Men that had rebelled from Melkor-worship, to stir up rebellion... and after his first fall to search out his hiding ( in which they failed ) and to cause ( ? dissension and disarray ) among the dark East… They must have had very great influence on the history of the Second age and Third age in weakening and disarraying the forces of East… who would both in the Second age and Third age otherwise have… outnumbered the West."
If this were the case, they would be allowed to return to Valinor. Which points out the problem with Tolkien's writings as they often changed and are contradictory. So it's up to the reader to decide because Tolkien hadn't done so before his death.
Beorn was fond of Radagast ("not bad for a wizard") and his son Grimbeorn could have very likely paired up with Radagast to defend the Beornings. You have to think that Sauron would not have forgotten or forgiven Beorn for killing Bolg during the Battle of the Five Armies. So my best guess is that Grimbeorn and Radagast stood side by side at the Ford of Carrock protecting the Beornings from a horde of goblins and wargs.