Helaman 8:21 And now will you dispute that Jerusalem was destroyed? Will ye say that the sons of Zedekiah were not slain, all except it were Mulek? Yea, and do ye not behold that the seed of Zedekiah are with us, and they were driven out of the land of Jerusalem? How did the people know for sure that Jerusalem had been destroyed as Lehi and his family had left before it was destroyed.
The very verse you listed explains the proof they had that Jerusalem was destroyed. But to understand it you need to know who Mulek and the Mulekites were.
The Book of Mormon contains the three groups coming to the Americas. The Nephites, who are the main focus, the Jaredites who are mainly in the Book of Ether, and then the Mulekites. Their journey is what I will focus on.
The bible records the destruction of Jerusalem during the rein of King Zedekiah and the killing of Zedekiah’s sons in 2 Kings 25:7.
“And they slew the sons of Zedekiah before his eyes, and put out the eyes of Zedekiah, and bound him with fetters of brass, and carried him to Babylon.”
Now the Book of Mormon claims in the verse you gave that there was one exception. One son survived. He witnessed the destruction and fled. God preserved him and brought him to the Americas.
When Mulek got here he could record his experiences, but they did not bring the record of his people with him. Over time and generations their language became corrupt, and their traditions that they had no records of, became distorted.
This was their state when the Nephites found them being lead by Zarahemla (a descendant of Mulek). The Nephites taught them the language and they learned how they came to be here. This showed the Nephites two very important things. It showed just how important it was that Nephi (the first one) and his brothers went back for the brass plates. And it provided a record of the destruction of Jerusalem from the accounts of Mulek.
That is what they are saying in Helaman 8:21. The Prophet Nephi (not the first one) is using the prophecy of the destruction of Jerusalem, which they can use the testimony of the Mulekites to prove what happened, to support the belief in the prophecy about Christ and His coming.