One quick thing, the massacre happened on 16-17th March 1190, not in 1189.

A bit of context might be helpful here. The growth of the crusading movement had led to a general increase in attacks against anyone who might be considered an enemy of God. The First Crusade saw pogroms throughout the Rhine area with thousands killed despite the efforts of local Christian clergy to protect Jewish populations. The Second Crusade had seen a similar outburst of violence that only stopped when the papacy sent Bernard of Clairvaux, by far the most respected clergyman in Europe, to shame the perpetrators. In 1179 the Catholic Church began to condone these attacks, as the 3rd Lateran Council decreed that Jews ought to be subservient to Christians and therefore may be legitimate targets of crusading. In 1189, Richard I began his preparations to embark on the Third Crusade, so Europe was already a deeply hostile place for Jews.

At his coronation ceremony, a group of Jews presented themselves to Richard but were attacked by an angry mob because some of them had barged in uninvited. An argument started, and this spiralled into a riot. Richard was livid, this was a dreadful start to his reign, but since he was about to go on a crusade he could not take serious action. He also quickly realised that many of the participants were prominent noblemen and as a new king he needed their support, so he could not punish many people. After this incident, people realised that the men who would be running the kingdom whilst Richard was crusading would not punish attacks on Jews. In the first year of Richard's reign there were attacks in Lynn, Stamford Fair, Bury, Lincoln, Colchester, Thetford, Ospringe, and of course York.

Throughout early 1190, there were sporadic assaults on Jews in York. As the departure date for the Third Crusade neared, this only got worse. Essentially, two of the most prominent Jews in York were akin to loan sharks. One of them, Benedict, was well known as a rather nasty man and was one of the men who barged into Richard's coronation. When Richard left for the Third Crusade, many people took oaths to attack Benedict and all those who associated with him (ie the entire Jewish community). There were also crusaders who had missed the leaving date and were eager to fight the enemies of God at home (ie the entire Jewish community). Finally, there were prominent members of the local community who owed a lot of money to Benedict, and sought to wipe out their debt by destroying the records and everyone who might vouch against them, so the entire Jewish community. Benedict had died in the riots in London, so destroying his records would wipe out all their debt. Another noteworthy Jew of York, Joceus, was also targeted for his moneylending activities. Although William of Newburgh's account is rather sympathetic to Jews in general, he personally believed that Jews ought to be subservient to Christians, and he had no issue with blaming Benedict and Joecus for giving the locals a reason to attack.

At some point a fire began in the city. William accepts that it could have just been chance, but he also puts forward a theory that it was arson by anti-Semites. The idea was that, whilst people were preoccupied by the fire, they would find and kill Jews throughout the city and blame them for the fire. It was certainly true that on the night of the fire, a mob broke into Benedict's house, looted everything, then burned it down. With the town militia engaged in firefighting in another part of the city, there was nothing to stop them. Following this event, Joceus approached the sheriff and asked if the Jews might take refuge in the castle. The sheriff, aware that Richard had passed a law requiring that sheriffs protect the Jews, obliged. Over the next few days the Jews of the city moved their possessions into the castle under armed protection. After a few days of this, a mob attacked Joceus' house at night and set it alight. Some people were still there packing belongings, and they were killed, but Joceus was at the castle at the time so he was unharmed.

Enraged by this, the small group who had begun these attacks raised a large armed mob. Those Jews who had remained outside the castle were killed or forced to convert. When the sheriff left the castle to see to another part of the city, the Jews refused to let him back in. William suggests that the Jews thought the sheriff was going to let the mob in either through weakness of character or incompetence, since he kept coming and going; making them open the gates several times a day. The sheriff was deeply offended by this and sought the help of a nearby nobleman with a retinue of knights. The nobleman was told about Jews seizing the castle, he was not told about the anti-Semitic mob. When he arrived at York he gave the order for the militia to assemble and take back the castle, but quickly saw that things were totally out of control. He attempted to order the mob to stand down, as it seems the reality of the situation had dawned on him, but the mob ignored him. A local clergyman of the Premonstratensian Order began preaching to the mob and encouraged them to attack. In doing so, he took over as leader of the mob. He encouraged the building of ladders and rams shouting 'Down with the enemies of Christ' as he personally moved a ram up to the walls. Hearing this, someone dropped a boulder on him. He was the only non-Jew to die in the siege.

On the night of the 16th March, it was clear that the mob would break down the gates the next day and kill everyone. An elder suggested that they go out on their own terms rather than be brutalised by the mob. The story of Jews killing themselves and each other rather than die to an enemy was a centuries old trope in Jewish literature, so the extent to which this occurred is debatable, but William certainly believed it was almost all of them and harshly condemned it. Some people certainly had opted for suicide, as the next day some Jews went up the battlements with their bodies and begged the mob to spare the rest. The mob was moved by this and nearly backed down and agreed that the Jews could live if they converted to Christianity. This agreement meant nothing though, for as soon as the Jews opened the gates they were slaughtered. Every Jew in York had been killed. The ringleaders then gathered any documentation of debts, went to the cathedral, and made the clergy absolve them of debt under threats of violence.

Needless to say, Richard I was not pleased. Upon hearing of the massacre he informed the regent and chancellor, the bishop of Ely, that the perpetrators should be tried for high treason and executed, and that an army should be gathered and sent to York to make the city submit to such trials. The ringleaders heard of the army in advance and fled, whilst the townsfolk all claimed that they had nothing to do with it and that everyone involved had fled to Scotland. Unable to prove otherwise, the chancellor extracted a heavy fine from every citizen, removed the sheriff and the authority of the nobleman who helped him, and left. William ends the passage by claiming that nobody was ever properly punished for their crimes.

You can read all of William's account here: https://sourcebooks.fordham.edu/basis/williamofnewburgh-four.asp#9