In general, you should be highly sceptical of specific dialogue included by medieval chroniclers. At best you're usually dealing with an author who is writing something from memory that they likely experience years prior, meaning that best case scenario they have a good memory and what they recorded got the gist of what was said if not the exact wording. However, medieval chroniclers didn’t often confine themselves to what really happened, especially with regard to heroic speeches and dialogue, and in many cases, it is best to interpret exact wording as an invention of the chronicler unless you have strong evidence that suggests otherwise, e.g. multiple different authors reporting essentially the same thing.

As for Ibn al-Athir specifically, he’s an interesting source. Ibn al-Athir lived between approximately 1160 and 1233, which makes him a contemporary of Saladin and about 70 years after the First Crusade. Note that he was born about 70 years after the First Crusade, by the time he was writing his chronicles it was probably more like 90-100 years after the First Crusade. He lived primarily in north-eastern Syria, moving between the cities of Mosul, Aleppo, and Damascus for the most part (just as a note, in Crusades Scholarship Syria is used to refer to this region more generally, and not specifically to areas within the modern country of Syria, so Mosul would be considered to generally be within Syria even though today it is in Iraq. Borders are tricky things).

This background is to point out that Ibn al-Athir was writing almost a century after the events he was describing from a city hundreds of miles away from Sicily, and in a different language from what King Roger would have been speaking. Best case scenario, Ibn al-Athir is working from another chronicle written by an eyewitness to Roger’s original speech, in which case you just have to hope that the initial author was accurate, that the scribe who translated it into Arabic knew what he was doing and both translated and transcribed it accurately, and that Ibn al-Athir chose to follow that source to the letter.

It’s a big ask for anyone, and far more likely Ibn al-Athir is simply inventing this speech for his own purposes. For one thing, the idea that Roger I of Sicily was the motivator behind the First Crusade pretty seriously contradicts the evidence we have from what Christian authors were writing in the Crusade’s immediate aftermath. Authors like Fulcher of Chartres, Raymond of Aguilers, and the anonymous author of the Gesta Francorum all give credit to a combination of Emperor Alexius and Pope Urban II, not the King of Sicily.

I don’t want to give the impression that Ibn al-Athir is some kind of dishonest liar who we should entirely mistrust, though. In this case he’s not providing a trustworthy account, but then I wouldn’t necessarily expect him to. I mentioned above that Ibn al-Athir was a contemporary of Saladin, and that’s an important fact. Ibn al-Athir’s chronicle is a history of the Islamic world from Mohammed to the (then) present day. The further back you go, the less reliable it’s generally felt that he is. You’ll rarely find scholars citing Ibn al-Athir as a source when writing about the First Crusade, for example, and when you do it’s because they believe that he might have had access to a now lost chronicle that was originally written closer to the time of the First Crusade and he seems to have largely copied it verbatim (unfortunately, I can’t think of any times this is specifically the case).

He’s sometimes used during discussions of the Second Crusade, because for various reasons there are far fewer sources for that Crusade so scholars are required to use ones that would otherwise be viewed as less reliable. Plus, the Second Crusade is much closer to Ibn al-Athir’s own lifetime – it was from approximately 1147-1150, so concluded only a decade before his birth meaning he would likely have been able to talk to people who had been alive for it and maybe even participated in it – and Ibn al-Athir was a retainer of the Zengid dynasty which would have given him access to information about things like the Conquest of Edessa by Zengi that many other authors might not have had. An eyewitness source would still be preferable, but Ibn al-Athir has a lot to offer in this area.

The real place where you’ll find Ibn al-Athir popping up all the time, though, is in histories of Nur al-Din and Saladin. Ibn al-Athir lived through Saladin’s rise to power, and held allegiance to the dynasty that Saladin replaced, and so provides an actual eyewitness account of those events. Now, we would still be very sceptical of any dialogue that Ibn al-Athir puts in Saladin’s mouth – after all, Ibn al-Athir wasn’t particularly close to the Sultan and wouldn’t have been following him around writing down everything he said – but by and large he is one of the most accurate contemporary accounts of that period.

I wish I could provide more context for why Ibn al-Athir chose to give the King of Sicily a more central role in the formulating of the First Crusade than he actually had, but I couldn’t provide a satisfactory answer without doing a bunch of research that I sadly don’t have time for. I’m sure there’s an interesting story to dig out of there – particularly around what Muslim perceptions of the King of Sicily were, as well as how much Ibn al-Athir actually may have known about Christian political intrigue – but I can’t provide more than an indication that it probably exists!

So far as I know the only complete translation of Ibn al-Athir’s chronicle into English is the one by D.S. Richards, which is far too recent to be freely available online (it was published over a few years starting in 2006). Some excerpts of his chronicle were included in Francesco Gabrieli’s Arab Historians of the Crusades, but that’s also too recent to be freely available online.

A great introduction to Muslim perspectives in the Crusades is Paul Cobb’s The Race for Paradise, while Carole Hillenbrand’s The Crusades: Islamic Perspectives is the definitive history of the subject.

In general, I recommend Thomas Asbridge’s The Crusades as my preferred introductory history, but Chris Tyerman’s God’s War and Jonathan Riley-Smiths The Crusades are both great as well.