а) Читая книгу, Иван не обращал внимания на то, что происходило вокруг.
б) Читая книгу, Иван не обращал внимания на то, что происходит вокруг.
Are both sentences correct? Do they have the same meaning?
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I don't think it has anything to do with relative clauses.
The second sentence is just an example of https://en.wikipedia.org/wiki/Historical_present in Russian. It's fine.
Do they have the same meaning?
They do. The second sentence may seem the slightest bit more lively, but that will likely depend on the context and the reader.