I think this date is actually 1628BC and the same time as the Jewish Exodus from Egypt. The volcano plume would have had to be 30 miles high to be seen from Egypt..."staff by day, torch by night."
The most recent eruption of Pinatubo in the Phillipines was 26 miles high and the one in/around Alaska was greater than 30 miles high.
Wasn't the whole idea of the pillar of smoke that it would be a directional marker that would lead them away from Egypt and toward the promised land?
I hate to rain on your theory connecting the Thera volcano and Exodus, but if the Israelites had followed the smoke they would have wound up going NORTH our of Egypt into the Mediterranean Sea.