It seems very plausible that the Santorini eruption could have a profound effect on all of the Mediterranean civilsations (and indeed those far removed).
Digging around on the Web it seems that the latest estimates on the date of the eruption are around 164500-1650BC, which is actually quite a while before the final demise of the Minoans - possibly as much as 150 years.
It is possible that the eruption led to failures of harvests around the world - there is apparently a Chinese report that fits in with this timescale. I imagine a nomadic people would be well placed to exploit the problems this would cause for established powers.
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