To answer the thread title's question, "Probably shortly after the destruction of the Second Temple." See, the reason there was a Jewish diaspora is that they'd revolted against Roman rule for like the hundredth time, and the Vespasian (who was officially sick of their shit) had his son Titus fuck up Jerusalem and kick out the Jews. So, having been kicked out of their homelands they went on to form ethnic enclaves all throughout the Roman empire, becoming ubiquitous in major cities all around the Med. So when you've got a tightly-knit, intelligent, insular community with a reputation for sharp business dealing scattered all throughout the known world, the idea of a conspiracy becomes superficially plausible, as they DO work together on a local level. That this cooperation scales up to "masterminding world events" is a rather dubious proposition, but it isn't obviously wrong in the way that making a similar claim about, say, Etruscans would have been.