Luke tells us in Acts 18:2 that Aquila and Priscilla had left Rome and come to Corinth due to the Jews being expelled from Rome by the Emperor Claudius. The problem is that some scholars try to date the expulsion of the Jews from Rome in 41 CE at the beginning of Claudius’ reign, citing Dio Cassius as their authority. Nevertheless, I believe there are stronger reasons for a later dating, including a fourth century Christian historian, Orosius, who used data from sources other than the Bible to date the expulsion to the ninth year of Claudius reign.
While Dio claims there was no actual expulsion of the Jews, Suetonius does claim Claudius expelled the Jews over disturbances developing among the Jews in Rome over Chrestus. So, they probably refer to two different events during Claudius’ reign. The Jews on other occasions had been expelled from Rome—most recently during the reign of Tiberius cir. 19 CE, so such a thing was not a unique occurrence which might prompt some to think Suetonius and Dio Cassius spoke of the same event.
When Claudius took the throne, he had some unfinished matters to attend to, which he inherited from Caligula. Among these was the problem that almost brought Rome and Jerusalem to war, namely a dispute between Jewish and gentile residents at Alexandria that escalated into Caligula’s threat to place his image in the Temple at Jerusalem. Long-story-short, he was assassinated before ruling on the matter, so it fell to Claudius who, probably seeking to cool down the tension in the eastern provinces, warned the parties concerned about future behavior, and appointed Agrippa as king and ruler over Judea. It was probably to this tension which, no doubt had reached Rome, that Dio Cassius refers, and not to the incident concerning Chrestus.
On the other hand, Suetonius refers to unrest at Rome among the Jews concerning Crestus. The name Chrestus is a Roman name and was quite common in the 1st century, but the fact that Suetonius doesn’t refer to ‘a certain Chrestus’ seems to imply this Chrestus was well known. It is difficult to believe that an historian such as Suetonius, writing in the 2nd century CE did not know about Christianity or its founder, Jesus also called Christ, and so made an error by writing Chrestus for Christus. However, Justin Martyr, an early church apologist living in the 2nd century CE, “attests to the fact that the name “Christianus” was occasionally spelled Chrestianus in Latin, and a wordplay with the Greek chrestos (G5543 meaning good, kind) is mentioned.” Therefore, knowing this, coupled with the strong probability that both Aquila and Priscilla were Christians before meeting Paul, it would seem probable that Claudius acted against the Jews in 49 CE. Luke’s mention that they had recently come from Rome due to the Jews being expelled (Acts 18:2), would put Paul’s arrival in Corinth sometime in 50 or 51 CE, probably 51 CE, since Luke has Paul appearing before Gallio (Acts 18:12), the Roman proconsul of Achaia, and the time of his service as proconsul is almost certainly fixed from July 51 to July 52 CE
 “As for the Jews, who had again increased so greatly that by reason of their multitude it would have been hard without raising a tumult to bar them from the city, he did not drive them out, but ordered them, while continuing their traditional mode of life, not to hold [open?] meetings” Dio Cassius 60.6.6 – sited from The Acts of the Apostles, page 539, by Ben Witherington.
 Orosius, Historia contra Paganos, 7.6.15; the 9th year of Claudius’ reign would fall between January 25, 49 CE to January 24, 50 CE; cited from Witherinton, The Acts of the Apostles, page 540.
 See Suetonius, Life of Claudius, 25.
 Josephus, Antiquities of the Jews, 18.3.5.
 Justin Martyr, Apology 1.3-4; see footnote in Witherington, The Acts of the Apostles, page 540.