The Baku oil fields were capitalized by the Rothschild banking dynasty, which was already immensely wealthy before the oil age. Perhaps others will weigh in, but as I recall this was in response to the fabulous wealth Rockefeller was realizing in the United States. Petroleum had always been present around Baku and elsewhere, but it hadn't been exploited on the same industrial scale. It was sometimes regarded as an inconvenience which devalued land.
Sure - I don't doubt that Baku made some people fabulously rich, I'm more curious about "most modern billionaires", specifically "most". I'm not even convinced that most modern billionaires made their billions through petroleum, much less Baku.
In this case, the Rothschilds were already a powerful European banking dynasty. There are many shadowy speculations about the different branches of this family. Perhaps this is where the confusion originates.
The Nobel family did better relative to their previous station. In the end the Baku concerns were sold to Rockefeller before being nationalized after the Russian Revolution.