Despite this evidence, the exact date of the eruption has been difficult to determine. For most of the twentieth century, archaeologists placed it at c. 1500 BCE, but this date appeared to be too young as radiocarbon dating analysis of an olive tree buried beneath a lava flow from the volcano indicate that the eruption occurred between 1627 BCE and 1600 BCE with a 95% degree of probability (Friedrich, Kromer, Friedrich, Heinemeier, Pfeiffer, Talamo, Science, 2006).
Plus or minus 10 years on 1613BC is 1623-1603BC.
Actually, for quite a while it was given as 1550, not 1500 contrary to Wiki. Not that it matters any at this point. In any case this date also has nothing to do with any alleged events c.2193 BC.