this is a passage from a roman writer named juvenal who lived roughly at the same time as the destruction of the second temple, which we can at least be sure actually happened
For the Syrian Orontes has long since polluted the Tiber,
Bringing its language and customs, pipes and harp-strings,
And even their native timbrels are dragged along too,
And the girls forced to offer themselves in the Circus.
the reality is that the romans took huge numbers of slaves from the region, and that roman slavery was both brutal and sort of liberal, in the sense that slaves were routinely emancipated. so, the end result is that the romans settled huge numbers of people from the middle east on the italian peninsula. and, i mean, just look at a picture of your classical, arian roman with his northern, alpine features and a picture of your modern day arab-looking italian and tell me that isn't fucking obvious.
that is what happened: the romans inherited a middle eastern cultural hegemony and eventually become subsumed by it, through both voluntary and involuntary migration from the middle east to western europe.
so, attaching jewish migration to the destruction of the temple is no doubt a glossing over of history. the event happened, and some migration was no doubt a direct consequence of it. but, migration in and out of the region - to spain and northern africa, especially - had been occurring for centuries previous to it. i mean, the carthaginian state in modern day tunisia was the force that truly built and urbanized spain (which was initially inhabited by indigenous basques and warlike tribal celtic groups) before it was romanized, and they were the sibling culture to the ancient jews; what the archaeology actually says is that the "jews" of the period before the captivity were essentially a forgotten backwater of phoenecian civilization and essentially worshipped phoenician gods and carried out phoenician cultural practices, and that judaism is an essentially iranian religion that entered the region after cyrus, wiping out what was left of ancestral phoenecian culture - which completely disappeared altogether, under first the persians and then the greeks, until the day that carthage was, indeed, destroyed.
so, it's a kind of oversimplification of history to assign all of this migration to this scattering event - the migration took place for centuries before 70 ce, and for centuries after it, as well. and, you can look this up yourself and find out that, yes, i'm summarizing experts, even if i'm too lazy to look it up right now.