It was a romantic narrative of some Eastern traveller of the thirties, pompous maybe, but fragrant with the emotion with which the East came to the generation that followed Byron and Chateaubriand.
It was not necessarily an Eastern writer, it could've been a European author writing about a journey through the East.
Since this author of the "romantic narrative" belonged to the generation that followed Byron and Chateaubriand, he saw the East in an emotional, romantic way. He was prepared to see the East in this way by these two authors who lived earlier. The meaning is that those two famous writers wrote so enthusiastically about the East (and about other matters) that the following generation, due to the popularity of their books, was taught to see the East (and probably some other matters) in an emotional, romantic way.
And then this following generation grew up, some of its members also became writers and in their books reflected this emotional view of the East.
We can explain the phrase
..the East came to the generation
as "the East came to be seen by the generation", or "the East came to this generation through the works of Byron and Chateaubriand", or "in the light of the works of Byron and Chateaubriand".
Charles Dickens's works, for example, were so popular around the world that
There was a particular emotion with which Britain and the city of London came to the generation that followed Dickens.