The Normans were indeed the descendants of Vikings, specifically of the group led by Rollo the Walker, who was granted lands in Normandy in exchange for defending France against other Viking attacks. They were fearsome warriors before they settled there - that was the whole point of settling them in Normandy. But that was in 911 AD, and there's a long gap between the Norman settlement of Normandy and the First Crusade, which was called in 1095, almost 2 centuries later. Norman knights in the late 11th century weren't Vikings, they were Normans.

The Norman response to the First Crusade was rather mixed. The Normans of England were frosty in their response, the Normans of Normandy joined in some numbers under Duke Robert, and some Normans in Italy joined the First Crusade under the banner of Bohemond, who at that time was arguably a robber baron (he had been disinherited, and was launching raids against his brother-in-law).

The Normans in England, generally speaking, were not that keen on the idea of the First Crusade. Some wrote to the Archbishop of Canterbury, Anselm, for guidance. Whilst Anselm stopped short of directly criticizing Pope Urban II, he did not think the expedition was a good idea. He chose not to preach the crusade as he was supposed to, which says a lot about his attitude. In his replies to monks and knights who sought his advice, Anselm implied that the promised remission of sins was not theologically sound, and that the idea that killing would ever be rewarded by God was a stupid one. He advised that, rather than go on crusade, god-loving knights should put down their swords and join a monastery. This seems to have been a fairly common view among the clergy of England and of the Norman knights there, as few English Normans went on the First Crusade even after Anselm was driven into exile. Preaching the crusade in England was not practical, as the king was hostile to the church, and the local clergy were generally either apathetic toward or against the crusade. Some Normans in England did join the expedition, such as Ivo Grandmesnil, the Sheriff of Leicester (and the loss of a sheriff was unlikely to make the king any friendlier to crusade preaching), but not many. The most notable English Norman to participate was Ralph de Gaël, the Earl of East Anglia, but he died in 1096 and played no major role, and his army wasn't noteworthy; a testament to the regional apathy toward the crusade.

The Normans in Normandy were moderate in their response, though this was mainly the result of Duke Robert II. He was keen to go on the expedition, and mortgaged the entire duchy to his brother in order to raise an army. This army was probably around 5000 men, perhaps slightly more, and of the crusading armies it was one of the most loyal. When a leader died or deserted, it was quite common for knights to place themselves under Robert's command because of Robert's commitment to the crusade. He was one of the major leaders, and did sign up pretty much right away because of his strong sense of religious commitment.

The Normans of southern Italy are generally thought to be the least pious in their motivations to join. Bohemond brought one of the largest and most experienced of the crusading armies, but he was not joining the campaign just out of piety. Bohemond used the crusade for his own political ends, carving out a principality for himself in the Holy Land. In exchange for Bohemond's help, Emperor Alexios I had offered him something in the east - we don't know exactly what, but it had something to do with Antioch and the land around it. Bohemond abandoned the crusade to rule Antioch, and did not accompany the army to Jerusalem. After the First Crusade, he would use his popularity to tour Europe in order to raise an army against the Byzantine Empire that the First Crusade was called to help.

So the Norman reaction to the First Crusade was not to join up 'pretty much at instant', and those who did throw aside their schedules to join the expedition (as Bohemond and Robert II did) sometimes had secular motivations. Frankly, the only powerful Norman nobleman who was fully committed to the idea was Robert II, Duke of Normandy. It is not known how many Norman knights, or what percentage, signed up. Norman knights did go on the crusade, but it's a lot more complicated than simple religious commitment, and they were outnumbered by other groups like the French and the peoples of the Low Countries.